Systems and methods for fabricating three-dimensional objects

ABSTRACT

Systems and methods for fabricating three-dimensional objects. The system includes an optical imaging system providing a light source; a photosensitive medium adapted to change states upon exposure to a portion of the light source from the optical imaging system; a control system for controlling movement of the optical imaging system, wherein the optical imaging system moves continuously above the photosensitive medium. The method includes moving a maskless optical imaging system providing the light beam in a continuous sequence; presenting the light beam on a portion of the photosensitive medium; lowering a plate upon which the photosensitive medium resides; and applying a new layer of the photosensitive medium.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit, under 35 U.S.C. §119(e), to U.S.Provisional Applications No. 61/723,991 filed Nov. 8, 2012. Thisapplication is also a Continuation-in-part of U.S. patent applicationSer. No. 12/435,776, which claims benefit, under 35 U.S.C. §119(e), ofU.S. Provisional Application Ser. No. 61/050,383, filed 5 May 2008. Theentire contents and substance of the above applications are herebyincorporated by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under grantsHR0011-07-1-0034 and HR0011-08-1-0075, awarded by the Defense AdvancedResearch Projects Agency (DARPA). The federal government has certainrights in the invention.

BACKGROUND

Rapid prototyping or solid free-form fabrication has become anincreasingly important tool, and is a technology that has seen greatadvances since its initial application in the 1980s, evidenced in U.S.Pat. No. 4,575,330, which is incorporated by reference herein as iffully set forth below. In one common embodiment known asstereolithography, rapid prototyping manufacturing makes use of a bathof curable liquid, wherein some movable point within the bath issubjected to stimulation by a prescribed curing source. As the source ismoved with respect to the bath or as the bath is moved with respect tothe source, the point that undergoes solidification or curing isconstantly made to move. The result is the construction of a solidifiedmass of cured material contained within the otherwise liquid bath. Theregion commonly solidified is positioned at or very near the surface ofthe bath in most practical applications. As the liquid is solidified,the solid structure is progressively lowered into the bath allowing theuncured liquid to flow over the surface, which is in turn subjected tothe same process. By continuing to solidify these very thin layers, thesolid object is built up into its final shape. Bonding of one layer to aprevious layer is an inherent property of the process as is known in theart.

For example, photolithography systems that direct light beams onto aphotosensitive surface covered by a mask, etching a desired pattern onthe substrate corresponding to the void areas of the mask, are known inthe art. In mask-based photolithography systems, the patterns generatedare defined by physical masks placed in the path of light used forphoto-activation. While effective, the use of physical masks inphotolithography has numerous drawbacks, including the cost offabricating masks, the time required to produce the sets of masks neededto fabricate semiconductors, the diffraction effects resulting fromlight from a light source being diffracted from opaque portions of themask, registration errors during mask alignment for multilevel patterns,color centers formed in the mask substrate, defects in the mask, thenecessity for periodic cleaning, and the deterioration of the mask as aconsequence of continuous cleaning.

Maskless photolithography systems are also known in the art and oftenuse an off-axis light source coupled with a digital micromirror array tofabricate chips containing probes for genes or other solid phasecombinatorial chemistry to be performed in high-density microarrays.

While maskless photolithography systems address several of the problemsassociated with mask-based photolithography systems, such as distortionand uniformity of images, problems still arise. Notably, in environmentsrequiring rapid prototyping and limited production quantities, theadvantages of maskless systems as a result of efficiencies derived fromquantities of scale are not realized. Further, while masklessphotolithography systems are directed to semiconductor manufacturing,these prior art systems and methods notably lack reference to otherapplications lending themselves to maskless photolithography techniques.

A commonly-used curable medium includes photopolymers, which arepolymerizable when exposed to light. Photopolymers may be applied to asubstrate or objects in a liquid or semi-liquid form and then exposed tolight, such as ultraviolet light, to polymerize the polymer and createsolid coatings or castings. In addition, conductive photopolymers areknown that exhibit electrically conductive properties, allowing creationof electric circuits by polymerizing the polymers in circuit layoutpatterns. Conventional methods of photopolymerization, however, usephysical masks to define areas of polymerization. This mask-basedphotopolymer process suffers from the disadvantages of mask-basedphotolithography methods, including the requisite need for manydifferent masks, long lead time for mask creation, inability to modifymasks, and the degradation of masks used in the manufacturing process.

As one may imagine, there are many advantages of rapid prototyping. Forexample, the rapid prototyping process has the ability to drasticallyreduce the time between product conception and final design, and tocreate complex shapes. More traditional modeling or prototyping isobtained from an iterative generation of a series of drawings which areanalyzed by the design team, manufacturing, the consumer, and perhapsothers, until a tentative final design results which is consideredviable. This agreed upon design is then created by casting and/ormachining processes. If molds are needed, these must be fabricated aswell, which may take considerable and valuable time. The finishedprototype is then tested to determine whether it meets the criteria forwhich the part was designed. The design and review process is oftentedious and tooling for the creation of the prototype is laborious andexpensive. If the part is complex, then a number of interim componentsmust first be assembled. The prototype itself is then constructed fromthe individual components.

Use of rapid prototyping significantly reduces the expense and timeneeded between conception and completion of the prototype. Commonly, theconcept is rendered in CAD (computer aided design). As this process isfully electronic, drawings are not required for fabrication. The CADsystem is used to generate a compatible output data file that containsinformation on the part's geometry. This file is typically convertedinto a “sliced” data file that contains information on the part'scross-section at predetermined layer depths. The rapid prototype controlsystem then regenerates each cross-section sequentially at the surfaceof the curable resin. The fabricated part may be analyzed by the team orused for various form, fit, and functional tests. Due to the rapid speedand low cost of the process, several designs may be fabricated andevaluated in a fraction of the time and for significantly less than itwould take to machine each concept. Because the rapid prototypingprocess creates the structure by the creation of very thin layers,complex components with internal complexities may be easily renderedwithout requiring the assembly of a plurality of individual components.

On the other hand, one conventional and significant disadvantage ofrapid prototyping, other than initial costs to implement technology, isthat the time associated with the creation of each part may still belonger than desired. Because creation of the part occurs in apoint-by-point, layer-by-layer process, the time necessary to produce asingle part may become excessive. Reduction in fabrication timescontinues to be a desirable goal. Though the above description pertainsto the process of stereolithography; the process, as well as the generaladvantages and disadvantages are similar for other rapid prototypingtechnologies.

SUMMARY

Embodiments of the present invention relate to optical modeling methodsand systems and, more particularly, to optical modeling methods andsystems in which a three-dimensional object is created by a continuouslymoving optical imaging source using a plurality of light beams toilluminate portions of a photo-curable medium. Furthermore, embodimentsof the present invention relate to systems and processes for large areamaskless photopolymerization (LAMP) using spatial light modulators(SLMs).

For example, a process/system of the present invention involves usingSLMs that scan at least a portion of the surface of a photopolymer. Inscanning a surface of the photopolymer, the SLMs project atwo-dimensional image (e.g., from a CAD file) thereon. Thetwo-dimensional image comprises a cross-section of a three-dimensionalobject to be formed within the various layers of the photopolymer, oncecured.

The process/system involves continuous movement of the SLMs, instead ofso-called “step and expose” or “step and repeat” movements. In providingcontinuous movement, the two-dimensional image projected by the SLMs isa dynamic image. That is, rather than projecting a fixed, single imageon a portion of the photopolymer surface, followed by movement of theSLMs to a new location, changing the SLMs to a new image thatcorresponds to the desired image over the new location, and projectionof the new image on the portion of the photopolymer surface at the newlocation, embodiments of the present invention involve projecting animage that continuously changes as the SLMs scan over the surface of thephotopolymer.

Embodiments of the present invention also provide optional features thatmay overcome some of the limitations of conventional systems andmethods, such as polymerization shrinkage, liquid polymer movement priorto being cured, and the like. Further, a combination of increasedresolution and speed of fabrication may be achieved. Examples ofimprovements in the LAMP systems that result in such properties may befound at least in the polymer container design, light modulationprocess, and light patterns.

The systems and processes above are not limited to photopolymers alone.For example, composite materials (e.g., those that contain a fillermaterial for the polymer), may be employed as well. Alternatively, if aceramic body is desired, a polymer-ceramic matrix may be used in theLAMP systems and processes, followed by removal of the polymericcomponent, thereby leaving behind a ceramic body that may be subjectedto additional processing.

These and other objects, features, and advantages of the presentinvention will become more apparent upon reading the followingspecification in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of a conventional foundry for investment castingof three-dimensional objects.

FIG. 2 is a pie chart of a conventional perfectly yielded investmentcast object.

FIGS. 3a and 3b are perspective views of a large area masklessphotopolymerization (LAMP) system, in accordance with an exemplaryembodiment of the present invention.

FIG. 4 is another perspective view of the LAMP system, in accordancewith an exemplary embodiment of the present invention.

FIGS. 5a-5c are an exemplary computer aided design slice pattern, inaccordance with an exemplary embodiment of the present invention.

FIGS. 6-7 are perspective view of the LAMP system for fabricating thethree-dimensional objects using a maskless optical imaging system, amaterial build platform, a material recoating system, and a controlsystem, in accordance with an exemplary embodiment of the presentinvention.

FIG. 8 is a perspective view of an optical imaging system for the LAMPsystem, in accordance with an exemplary embodiment of the presentinvention.

FIGS. 9a-9e illustrate a plurality of cross-sectional views of athree-dimensional computer aided design drawing, in accordance with anexemplary embodiment of the present invention.

FIG. 10a illustrates a plurality of stacked cross-sectional views of thetwo dimensional computer aided design drawings, in accordance with anexemplary embodiment of the present invention.

FIG. 10b illustrates a perspective view of a three-dimensional objectfrom the stacked cross-sectional views of the two-dimensional computeraided design drawings of FIG. 10a , in accordance with an exemplaryembodiment of the present invention.

FIG. 11 illustrates one embodiment of a LAMP machine having agantry-style scanning maskless optical imaging system in accordance withvarious aspects described herein.

FIG. 12 illustrates one embodiment of a scanning maskless opticalimaging system in accordance with various aspects described herein.

FIG. 13 illustrates one embodiment of a scanning maskless opticalimaging system in accordance with various aspects described herein.

FIG. 14 illustrates one embodiment of a material build platform (MBP) inaccordance with various aspects described herein.

FIGS. 15a-15c illustrate one embodiment of a material recoating system(MRS) in accordance with various aspects described herein.

FIGS. 16a-16c illustrate another embodiment of a material recoatingsystem (MRS) in accordance with various aspects described herein.

FIG. 17 illustrates a loss of build precision using a material recoatingsystem having a single-edge recoater.

FIGS. 18a-18e illustrate one embodiment of a material recoating systemhaving a multiblade recoater in accordance with various aspectsdescribed herein.

FIGS. 19a-19c illustrate one embodiment of a screen printing-styleinking window pane in accordance with various aspects described herein.

FIGS. 20a-20d illustrate a loss of build precision using a materialrecoating system.

FIGS. 21a and 21b illustrate one embodiment of a method of constructinga conformal lattice in an inter-part space using break lines inaccordance with various aspects as described herein.

FIGS. 22a-22h illustrate another embodiment of a method of constructinga conformal lattice in inter-part space using break lines in accordancewith various aspects as described herein.

FIGS. 23a-23f illustrate one embodiment of a LAMP machine in accordancewith various aspects as described herein.

FIGS. 24a and 24b illustrate one embodiment of a method for correcting agap error in accordance with various aspects described herein.

FIGS. 25(1)-25(3) illustrate another embodiment of a method forcorrecting a gap error in accordance with various aspects describedherein.

FIGS. 26(1)-26(4) illustrate one embodiment of a method of automatedpart layout and scaffolding in accordance with various aspects describedherein.

FIG. 27 illustrates one embodiment of a method of identifying a floatingisland in accordance with various aspects as described herein.

FIG. 28 illustrates one embodiment of a method of identifying amultifunctional support structure in accordance with various aspects asdescribed herein.

FIG. 29 illustrates one embodiment of a method for screening forshrinkage relief and support structures in accordance with variousaspects as described herein.

FIGS. 30a-30e illustrate another embodiment of a method for screeningfor shrinkage relief and support structures in accordance with variousaspects as described herein.

FIGS. 31a-31d illustrate another embodiment of a method for screeningfor shrinkage relief and support structures in accordance with variousaspects as described herein.

FIG. 32 provides a chart of screening-based grayscale working curves forone embodiment of a LAMP system.

FIG. 33 provides a chart of screening-based grayscale working curves forone embodiment of a LAMP system.

FIG. 34 provides a chart of screening-based grayscale working curves forone embodiment of a LAMP system.

FIG. 35 provides a chart of screening-based grayscale working curves forone embodiment of a LAMP system.

FIG. 36 provides a chart of screening-based grayscale working curves forone embodiment of a LAMP system.

FIG. 37 provides a chart of screening-based grayscale working curves forone embodiment of a LAMP system.

FIGS. 38a-38f illustrate one embodiment of a method of performing directslicing in accordance with various aspects as described herein.

FIG. 39 illustrates one embodiment of a method of identifying the“interior” from the “exterior” in accordance with various aspects asdescribed herein.

FIG. 40 is a slice image having rough edges due to floating point errorsin counting a distance traveled.

FIG. 41 illustrates test parts used in much of the previously reportedwork in the direct slicing literature.

FIG. 42 shows a CAD model of a typical internally cooled HP turbineblade.

FIG. 43a provides a chart of the number of stray lines observed in eachimage from a stack of hundred consecutive slices produced at twodifferent ACIS resolutions.

FIG. 43b provides a graph of the time to compute one slice scaling withDPI.

FIG. 44 shows the various elements of the BRep (Boundary Representation)data structure.

FIGS. 45a-45c illustrate a corner table data structure in accordancewith various aspects described herein.

FIGS. 46a-46b show a schematic of a cell structure used to identifyredundant vertices in accordance with various aspects described herein.

FIG. 47 is a flow chart of a method used to fill V[c] in accordance withvarious aspects described herein.

FIG. 48 provides a trend of this scaling with respect to the number offacets.

FIG. 49a illustrates a method for identifying the intersecting facets atan arbitrary Z-height in accordance with various aspects as describedherein.

FIG. 49b illustrates a data structure used for direct slicing of STLfiles in accordance with various aspects as described herein.

FIG. 49c illustrates computational time scaling with respect to a numberof facets.

FIG. 50 illustrates a data structure used to store these intersectionpoints in accordance with various aspects as described herein.

FIG. 51 illustrates slicing time scaling with respect to mesh size.

FIGS. 52a and 52b illustrate a particularly bad instance of stray lineerrors.

FIGS. 53a-53c illustrate a method of rectifying multi-pixel wide rowswith stray lines in accordance with various aspects as described herein.

FIGS. 54a-54c illustrate a method of tiling in accordance with variousaspects as described herein.

FIG. 55 illustrates the staircase effect while two created contours aresame size in inner area.

FIG. 56 illustrates a cusp volume for a hemispherical part.

FIGS. 57a-57f illustrate each of these steps for calculating the volumedeviation while slicing a sample CAD part in accordance with variousaspects as described herein.

FIG. 58 is a sample CAD part adaptively sliced using the volumedeviation approach.

FIG. 59 provides a chart of variation of layer thickness vs. height zfor sample part.

FIG. 60 provides a chart of the percentage volume deviation vs. heightfor sample part.

FIG. 61 provides a chart of percentage total volumetric error vs. heightfor sample part.

FIGS. 62a and 62b illustrate stair stepping caused on downward facingsurfaces while using all white build images.

FIGS. 63a-63d illustrate a method for producing a gray scale image inaccordance with various aspects described herein.

FIGS. 64a and 64b illustrate gray scale exposure results.

FIG. 65 illustrates a sample exposure image with a known constant squarelength with ten different tiles.

FIG. 66 illustrates cured squares obtained by exposing the image in FIG.65.

FIG. 67 shows the native orientation of the blade mold.

FIG. 68 illustrates a build orientation that reduces overhangs observedin the original orientation.

FIG. 69 illustrates a build orientation that reduces overhangs observedin the original orientation.

FIG. 70 illustrates a cross-section of the part as the base of theleading edge cavity is being built.

FIGS. 71a and 71b illustrate 3D slices of successive layers at thelocation corresponding to the floating island shown in FIG. 70.

FIG. 72 illustrates various supports generated on the sample HP bladeshown in FIG. 67 using this method.

FIGS. 73a and 73b illustrate a temperature profile obtained on theinternal wall of a leading edge with and without a support structure.

FIGS. 74a and 74b illustrate velocity streamlines in internal cavities.

FIGS. 75a and 75b illustrate a loss of build precision using a materialrecoating system having a single-edge recoater.

FIGS. 76a-76d illustrate one embodiment of a material recoating systemhaving a multiblade recoater in accordance with various aspectsdescribed herein.

FIGS. 77a-77c illustrate one embodiment of a screen printing-styleinking window pane in accordance with various aspects described herein.

FIGS. 78a-78f illustrate one embodiment of a LAMP machine in accordancewith various aspects as described herein.

FIG. 79 illustrates one embodiment of a LAMP machine in accordance withvarious aspects described herein.

FIG. 80 illustrates one embodiment of a LAMP machine in accordance withvarious aspects described herein.

FIG. 81 illustrates one embodiment of a LAMP machine in accordance withvarious aspects described herein.

FIG. 82 illustrates one embodiment of a LAMP machine material buildplatform in accordance with various aspects described herein.

FIG. 83 illustrates one embodiment of a LAMP machine material buildplatform in accordance with various aspects described herein.

FIG. 84 illustrates one embodiment of a LAMP machine material buildplatform substrate and substrate mount in accordance with variousaspects described herein.

FIG. 85 illustrates one embodiment of a LAMP machine material buildplatform substrate and substrate mount in accordance with variousaspects described herein.

FIG. 86 illustrates one embodiment of a LAMP machine material buildplatform substrate and substrate mount in accordance with variousaspects described herein.

FIG. 87 illustrates one embodiment of a LAMP machine material recoatingsystem in accordance with various aspects described herein.

FIG. 88 illustrates one embodiment of a LAMP machine material buildplatform seal system and material recoating system in accordance withvarious aspects described herein.

FIG. 89 illustrates one embodiment of a LAMP machine material buildplatform seal system and material recoating system in accordance withvarious aspects described herein.

FIG. 90 illustrates one embodiment of a LAMP machine material buildplatform seal system and material recoating system in accordance withvarious aspects described herein.

FIG. 91 illustrates one embodiment of a LAMP machine material buildplatform seal system and material recoating system supply reservoir inaccordance with various aspects described herein.

FIG. 92 illustrates one embodiment of a LAMP machine material recoatingsystem supply reservoir and recoater in accordance with various aspectsdescribed herein.

FIG. 93 illustrates one embodiment of a LAMP machine material recoatingsystem supply reservoir and recoater in accordance with various aspectsdescribed herein.

FIG. 94 illustrates one embodiment of a LAMP machine material buildplatform seal, material recoating system supply reservoir and recoaterin accordance with various aspects described herein.

FIGS. 95a-95c illustrate an embodiment for employing a series of imagingheads that move concurrently across the surface of a resin in accordancewith various aspects as described herein.

FIG. 96 illustrates an embodiment of for employing a two dimensionalarray of imaging heads to simultaneously pattern the surface of theresin in accordance with various aspects as described herein.

FIG. 97 provides a graph of the emission spectrum of a light source usedin an embodiment of LAMP.

FIG. 98 provides a comparison of the grayscale factor resulting from ascreened grayscale image at different screening resolutions.

FIGS. 99a-99f illustrate intensity distributions and profiles for (a) 1pixel, (b) 2 pixel, (c) 3 pixel, (d) 4 pixel, (e) 5 pixel, and (f) 10pixel line projections from the SLM.

FIG. 100 illustrates a light intensity distribution resulting from anall white projection.

FIG. 101 provides a chart of cure depth measurements at a fixed exposuretime and screening resolution as the grayscale was varied from 30% to90% white.

FIG. 102 illustrates a schematic for cure depth measurements with theincorporation of neutral density filters to determine the curingcharacteristics at different light intensities.

FIG. 103 provides a chart of working curves of a PCMS with exposure todifferent light intensities.

FIGS. 104a and 104b illustrate a summary of the dependence of thecritical energy and resin sensitivity on light intensity.

FIG. 105 provides a chart of working curves for various grayscale valuesand screening resolutions.

FIGS. 106a-106j provide a summary of the critical energy and resinsensitivity for various grayscale values and screening resolutions.

FIGS. 107a and 107b provide a graph summarizing the influence of lightintensity on curing characteristics resulting from homogenous grayscaleexposure.

FIG. 108 illustrates a checkerboard pattern that can be used to extractdimensional information.

FIGS. 109a-109d show images of checkerboard exposure at 600 ms withvarious square lengths to illustrate a homogenous transition.

FIG. 110 provides a chart illustrating homogenous transition of a PCMSresulting from a checkerboard exposure pattern.

FIGS. 111a-111d show images of a checkerboard exposure at 170 μm squarelength with various exposure times to illustrate the time dependence ofthe homogenous transition.

FIG. 112 provides a chart of exposure time working curves for selectedscreening resolutions.

FIGS. 113a and 113b provide a chart summarizing the trends in thecritical exposure time and resin sensitivity at screening resolutionswithin the homogenous transition.

FIG. 114 illustrates a schematic of material system resolution, wherethe projected pattern has features finer than the “pixel” of thematerial system, which can be defined by the scattering length.

FIGS. 115a-115d illustrate simulated light intensity distributionexperienced by the PCMS for selected checkerboard screening resolutions.

FIGS. 116a-116d provide charts comparing experimental cure depthmeasurements with the scattering length pixel model for predicting thelight intensity for grayscale and homogenous transition exposure.

FIGS. 117a and 117b provide a chart showing the degree of conversion andrate of polymerization for the PCMS at selected grayscale intensities of100%.

FIG. 118 provides a chart characterizing the influence of screeningresolution on the degree of conversion.

FIGS. 119a-119e show iteration steps in the development of grayscalesupport structures.

FIGS. 120a-120e show the results of a trial of fabricating unsupportedgeometries using grayscale support structures with various grayscalevalues.

FIGS. 121a-121c show images for a test of selective etching for achallenge component.

FIGS. 122a-122e show images of fabrication of a test component usingvarious grayscale values.

FIGS. 123a and 123b show images of results from print-through mediatedalternating GSS.

FIGS. 124a-124d show stereomicroscope images of an airfoil mold with“fissures.”

FIGS. 125a and 125b provide a schematic of the shrinkage mechanismsoccurring for one embodiment of a LAMP system.

FIG. 126 shows an image of curvature induced by UV illumination within asingle layer exposure.

FIGS. 127a-127d provide a schematic of a hollow cylinder design used toinvestigate methods to reduce defects in LAMP components.

FIGS. 128a and 128b show the result from fabrication of a test cylinderwith all white exposure for one embodiment of a LAMP system.

FIGS. 129a and 129b show the result from fabrication of a test cylinderwith all white exposure after BBO and sintering for one embodiment of aLAMP system.

FIGS. 130a-130c show green body molds for cylinders fabricated withcheckerboard exposure at selected square lengths for one embodiment of aLAMP system.

FIGS. 131a-131c show the effects of BBO and sintering on the testcylinders fabricated using a staggered checkerboard exposure with squarelength after BBO and sintering for one embodiment of a LAMP system.

FIGS. 132a-132d show test cylinders exhibiting vertical cracks for oneembodiment of a LAMP system.

DETAILED DESCRIPTION

To facilitate an understanding of embodiments, principles, and featuresof the present invention, they are explained hereinafter with referenceto implementation in illustrative embodiments. In particular, they aredescribed in the context of being a continuously moving rapidprototyping system and method.

Embodiments of the present invention, however, are not limited to use inthe described systems. Rather, embodiments of the present invention maybe used when a three-dimensional prototype object, e.g., a casting, isdesired or necessary. Thus, the system described hereinafter as acontinuously moving rapid prototyping system and method may also findutility as a system for many applications and for many sized objects.

The components described hereinafter as making up the variousembodiments are intended to be illustrative and not restrictive. Manysuitable components that would perform the same or a similar function asthe materials described herein are intended to be embraced within thescope of embodiments of the present invention.

FIG. 1 illustrates a conventional foundry flow chart for investmentcasting of three-dimensional objects. For example, the flow chartillustrated in FIG. 1 could be utilized to create turbine airfoils;turbine airfoils with extremely complex interior cooling passages areoften produced by investment casting. The exterior airfoil shape isdefined by injection molded wax patterns that are removed or “lost”after shelling. The interior passages of the airfoil are defined byinjection molded ceramic cores that are removed or “lost” after casting.The core and wax molding operations require sophisticated tooling,leading to excessive initial and maintenance costs, very slowfabrication cycles, and low casting yields.

The process 5 of FIG. 1 begins with the creation of all the tooling 10necessary to fabricate the cores, patterns, mold, and setters forcasting the items, typically involving over a thousand tools for eachitem. The next step involves fabrication 12 of ceramic cores byinjection molding. Molten wax may also be injection molded 14 to definethe patterns for the object's shape. Several such wax patterns are thenassembled 16 into a wax pattern assembly or tree. The pattern assemblyis then subjected to multiple rounds of slurry coating 18 and stuccoing20 to form the completed mold assembly. The mold assembly is then placedin an autoclave for dewaxing 22. The result is a hollow ceramic shellmold into which molten metal in poured to form the castings 24. Uponsolidification, the ceramic mold is broken away and the individual metalcastings are separated therefrom. The castings are next finished 26, 28,30 and inspected 32 prior to shipment 34.

As a result of the embodiments of the present invention, conventionalcasting steps 10, 12, 14, 16, 18, 20, 22 are obsolete, resulting in theelimination of over 1,000 tools and five major process steps ofthree-dimensional item prototyping.

As mentioned, there are major obstacles for conventional rapidprototyping. For example, despite the maturity of current investmentcasting practices, particularly in the aerospace industry, a majorchallenge exists in the affordable, high-yield, production of cooled,single crystal nickel-superalloy turbine airfoils for jet engines. Whilemany improvements in the performance of designs have been made, noknown, significant improvements have been made to lower the cost ofmanufacturing turbine airfoils. Improvements in turbine airfoil designshave vastly outpaced commensurate improvements in investment castingcapability.

In gas turbine engines, for example, it is well established that theturbine engines may achieve higher performance, such as greater powerdensity and lower Specific Fuel Consumption (SFC) by operating at highertemperatures. Turbine airfoils lay at the heart of gas turbine engines,operating at the highest temperatures—even in excess of their meltingpoint. Because turbine airfoils are subjected to very high heat, therehas been a continuing effort to identify improvements to the design,materials, and coatings for turbine airfoils to achieve even highertemperature capability and thus higher performance—typically at thesacrifice of affordability. Over the past four decades, materials haveimproved from wrought alloys to fourth generation single crystalsuperalloys; designs have improved from uncooled solid airfoils tohighly convectively effective and highly film effective, impingementcooled airfoils; and coatings have been developed to environmentally andthermally protect airfoils. Although commensurate manufacturing methodshave been developed to make more sophisticated alloys, designs, andcoatings producible, very little has been done to reduce the costs ofthese manufacturing processes, particularly investment castings, orrapid prototyping.

The cost of investment casting an object, e.g., a turbine airfoil, isestablished by material usage, and handling and finishing costs, but thefinal “sell” price is primarily driven by casting yield (cost of poorquality). To dramatically lower the sell price of manufacturing ofobjects, improvements of embodiments of the present invention may bemade in casting yield and secondarily through a reduction in handling,which also impacts casting yield. As shown in FIG. 2, for a perfectlyyielded investment cast object, typically a third of the cost iscomprised of manufacturing the integral core/shell “lost” mold (steps10-22 of FIG. 1); a third of the cost is metal pouring; and a third ofthe cost is finishing, gauging, and inspecting the finished metalcasting. Where casting yield is low, however, the cost of makingintegral core/shell molds dominates more of the overall costs, sometimescommanding up to half of the cost of an investment casting. In sum, fora yielded object casting, cost is evenly divided among manufacturing themold, casting, and finishing, as illustrated in FIG. 2.

The cost of manufacturing the “lost” integral core/shell is a large partof the cost of an investment cast object because approximately 60-90%percent of the causes for low casting yield occur in fabrication andhandling of the cores 12, wax injection 14 and dewaxing 22; whereasrelatively less scrap is typically caused by metal pouring andfinishing, steps 24, 26, 28, 30, 32, 34. Causes are typically due to theenormous amount of handling and handling-induced variation and damagethat occurs in the fabrication of cores, injection of wax around thecores, and subsequent high stresses placed on the cores during dewaxing.Core fracture and breakage, hand finishing breakage, waxinjection-induced core fracture, breakage and shift, and core shift andshell defects caused during dewaxing typically lead to downstream yieldproblems such as kiss-out, miss-run, recrystallized grains, surfacedefects, inclusions, and other defects detected after casting.Unfortunately, early causes for low casting yield are not discovereduntil after the metal has been cast, the shell and core removed, and themetal component is inspected.

Although some incremental productivity improvements have been made, suchas semi-automated finishing and handling, none have dramatically loweredthe cost of investment casting turbine airfoils. Elimination of the“lost” processes and accompanying tooling and handling by directlydigitally manufacturing the investment casting mold may dramaticallyincrease production yields, reduce costs and lead-times.

Embodiments of the present invention relate to systems and methods thatdevelop a disruptive manufacturing technology for the direct digitalmanufacturing (DDM) of three-dimensional items or objects, such asairfoils. Embodiments of the present invention are based on large areamaskless photopolymerization (LAMP) of photocurable materials (e.g.,photopolymers alone, composites comprising a photopolymer, ceramic- orceramic-precursor-filled photopolymers, metals, and the like).

As mentioned, referring to FIG. 1, LAMP may be used, in someembodiments, to produce integral ceramic cored molds ready for step 24,i.e., the casting step. As such, DDM of items using LAMP will replaceand thus eliminate steps 10-22, amounting to the elimination of over1,000 tools and five major processes with a single step corresponding todirect digital mold production. Accordingly, LAMP will fundamentallyeliminate at least approximately 95% percent or more of tooling andtooling costs, at least approximately 20-30% of the overall part cost,and at least approximately 60-90% of the causes for low casting yield.LAMP may enable in situ casting of more sophisticated features, such asfilm cooling holes, that are otherwise difficult or physicallyimpossible to cast with conventional investment casting processes,further improving casting yield and dramatically improving downstreammachining yields and costs.

Exemplary embodiments of the present invention relate to a both a systemand a method for fabricating a three-dimensional object.

In an exemplary embodiment, the system for fabricating athree-dimensional object includes an optical imaging system forproviding a light source, a photosensitive medium that is adapted tochange states, and a control system for continuously moving the opticalimaging system above the medium. The optical imaging system may use aspatial light modulator (SLM) to scan a portion of the surface of themedium housed in a container. In an exemplary embodiment, the medium isa photopolymer. As the optical imaging system scans the medium, when thelight source illuminates a portion of the surface of the medium, thecharacteristics of the medium change, e.g., from a liquid or aqueousstate to the solid state.

In an exemplary embodiment, the optical imaging system or radiationsystem includes a light source, a reflector system, an optical lenssystem, a mirror, the SLM comprising a digital mirror device (DMD), anda projection lens. In operation, the light source may illuminate anultraviolet light source, e.g., having a particular, predeterminedwavelength in the UV spectrum. Various embodiments of the presentinvention may include light sources comprising any one of an ultravioletlight, violet light, blue light, green light, actinic light, and thelike. The light emitting from the light source may be directed upon aportion of the reflector system, and thus reflects from the reflectorsystem, which may comprise a concave-shaped reflector. The reflector ofthe reflector system directs the light through a lens of the opticallens system before it reaches a mirror. The mirror then reflects thelight towards the digital mirror device (DMD). The DMD is amicroelectromechanical device comprising a plurality of tiny mirroredsurfaces that each may be independently pivoted from a first to a secondposition. The mirrors are formed into the surface of a semiconductorchip and through the application of an appropriate voltage to thecircuitry built under each mirror, that mirror may be made to tilt toone side or another with respect to a plane normal to the semiconductorchip. With respect to some fixed frame of reference, pivoting in onedirection causes the mirror to reflect light whereas pivoting in theopposite direction causes the light to be deflected from the fixed frameof reference. The light from the DMD is next directed towards aprojection lens. The light then is projected onto the surface of themedium in the container. Other types of SLMs, such as liquid crystaldisplays, grating light valves, and the like, may also be implemented.

For example, one process/system involves using SLMs that scan at least aportion of the surface of a photopolymer. In scanning a surface of thephotopolymer, the SLMs project a two-dimensional image (e.g., from a CADfile) thereon. The two-dimensional image comprises a cross-section of athree-dimensional object to be formed within the various layers of thephotopolymer, once cured.

The process/system involves continuous movement of the SLMs, instead ofso-called “step and expose” or “step and repeat” movements. In providingcontinuous movement, the two-dimensional image projected by the SLMs isa dynamic image. That is, rather than projecting a fixed, single imageon a portion of the photopolymer surface, followed by movement of theSLMs to a new location, changing the SLMs to a new image thatcorresponds to the desired image over the new location, and projectionof the new image on the portion of the photopolymer surface at the newlocation, embodiments of the present invention involve projecting animage that continuously changes as the SLMs scan over the surface of thephotopolymer.

As alluded to above, the systems and processes above are not limited touse of photopolymers as the photosensitive medium alone. For example,composite materials (e.g., those that contain a filler material for aphotopolymer, or those that combine the photopolymer with anotherpolymer), may be employed as well. For example, if a ceramic body isdesired, a polymer-ceramic matrix or a polymer-ceramic precursor matrixmay be used in the LAMP systems and processes, followed by removal ofthe polymeric component, thereby leaving behind a ceramic green bodythat may be subjected to additional processing.

The well-known approach of exposing a photosensitive medium with afocused, raster scanning laser beam is used in conventionalstereolithography systems, as well as in microelectronics manufacturingsystems for mask writing, prototyping, customization of chips, andrepair of defects. Such systems expose all the pixels one at a time onthe substrate. The most widely used direct-write systems use anultraviolet (UV) laser source. The laser source is focused to thedesired spot size on the surface of the polymer to be cross-linked orthe ceramic suspension to be photo-formed in stereolithography, or on asubstrate coated with a photosensitive material in the platesettingprint industry, or on a substrate coated with photoresist inmicroelectronics manufacturing. The focused spot may be modulated as thebeam is raster scanned across the substrate. In principle, these aremaskless systems. Because transfer of the pattern information by suchtools takes place in a slow, bit-by-bit serial mode, typical substrateexposure times may range from several minutes to several hours persquare foot. Some raster-writing tools use multiple rastering beams toovercome the low-throughput problem, while only partially achieving theobjective. Other raster-writing tool concepts have been developed in thelast few decades, but due to their low throughputs, all such systems aresuitable only for low-volume or one-of-a-kind applications such asprototyping or mask fabrication, and are unattractive for cost-effectivemanufacturing in high or even moderate volumes.

In an exemplary embodiment, the SLM is a two-dimensional array ofapproximately one million micro-pixels, each of which may beindividually turned ON or OFF. In the ON position, illumination that isincident on the pixel is directed toward a high-resolution projectionlens and imaged onto the photosensitive medium. In the OFF position, theillumination incident on the pixel is deflected away from the entrancenumerical aperture (NA) of the projection lens and not permitted toreach the substrate. The SLM is controlled by the control system, whichmay include a computer. The computer accesses CAD files containing theON/OFF states for all of the pixels in an entire frame, e.g., a bitmapframe.

Computer-to-conventional plate (CtCP) lithography technology may utilizeSLMs as programmable, massively parallel write-heads, as illustrated inFIGS. 3a and 3b . In an exemplary embodiment, the CtCP system may bemanufactured by BasysPrint's UV Series 57F machine equipped with asingle DMD-based scanning head, which was commercialized in the early2000s. The success of this technology led to the 700 series UVplatesetters with two DMD-based scanning heads working in tandem toachieve process throughput that was orders of magnitude higher thansingle laser beam writing techniques.

FIGS. 3a and 3b illustrate a perspective view of an optical imagingsystem providing a light source to a given surface, in accordance withan exemplary embodiment of the present invention. The LAMP system 100for fabricating a three-dimensional object includes the optical imagingsystem 200. The optical imaging system 200 or radiation system includesa light source 205, a reflector system 210, an optical lens system 215,a mirror 220, at least one SLM 225, e.g., a DMD, and a projection lens230.

The light source 205 may illuminate, and thus provide a light. Variousembodiments of the present invention may include light sourcescomprising any one of an ultraviolet light, violet light, blue light,green light, actinic light, and the like. In an exemplary embodiment,the light source has a particular, predetermined wavelength in the UVspectrum. Embodiments of the present invention may be described hereinas a UV light source, but embodiments of the present invention are notlimited to such a light source, and other light sources, including theexamples disclosed may be implemented.

The light emitting from the light source 205 may be projected upon aportion of the reflector system 210, and reflects from the reflectorsystem 210, which may comprise a concave-shaped reflector 211. Thereflector 211 of the reflector system 210 directs the light through alens 216 of the optical lens system 215 before it reaches the mirror220. The mirror 220 then reflects the light towards the DMD 225. Thelight from the DMD 225 is next directed towards the projection lens 230.The light from the projection lens 230 is then projected onto thesurface 300 of the photosensitive medium.

In an exemplary embodiment, the BasysPrint device may incorporate theoptical imaging system. In such an embodiment, BasysPrint's massivelyparallel scanning device may include a single DMD-based SLM. If desiredand/or necessary, the BasysPrint device may be extended to multiple DMDsworking in parallel.

FIG. 4 illustrates a perspective view of an exemplary embodiment of theoptical imaging system 200 emitting a light source onto a given surface300 of the photosensitive medium. In essence, FIG. 4 illustrates aschematic of an SLM-based CtCP scanning maskless imaging system.

In an exemplary embodiment, the UV light source 205 may be a mercuryvapor lamp, xenon lamp, violet laser diode, diode pumped solid statelaser, frequency-tripled Nd:YAG laser, XeF excimer laser, or the like.The UV light source 205 may illuminate an SLM or an array of SLMs, e.g.,one by two, such that the beams reflected from the ON pixels of the SLMarray are coupled into the projection lens while the beams from the OFFpixels are directed away from the lens. The elements of the SLM, e.g., aDMD, 225, nominally approximately 15 micrometers (μm) square in size,are individually controllable by the CAD data from the computer,enabling rapid, programmable selection of a large number of sites forlaser irradiation. The DMD 225 may modulate the illumination by means ofits bi-stable mirror configuration, which, in the ON state, directsreflected illumination toward a projection lens, and in the OFF state,directs illumination away from the lens.

The entire optical imaging system 200 may be mounted on an XY scanningstage with a large area of travel spanning several hundred millimeters.As the optical imaging system 200 is scanned over different areas of themedium, e.g., the substrate 300, the projection lens 230, with theappropriate magnification or reduction, images the ON pixels of the SLMarray directly onto the substrate 300. The projection lens 230 reductionratio may be between approximately 1 and approximately 50, which mayresult in a minimum feature size between approximately 15 microns andapproximately 0.3 microns. Each pixel in the array is digitallycontrolled to be either ON or OFF. A desired pattern corresponding to aninput bitmap image (e.g., BMP, TIFF, and the like files) may begenerated by the SLM by loading the array with bitmap data thatconfigures each pixel. When a different pattern is needed, a differentbitmap data set may be loaded. In effect, the SLM may be a rapidlyprogrammable structured light pattern generator that may reproduce anentire bitmap image with high fidelity across a large area substrate.

Comparing SLMs to serial exposure via laser direct-write techniques,SLMs enable massively parallel processing by exposing an entire imagefield in a single shot. The digital signal processing electronicsintegrated into commercial SLMs may support a high frame rate (severalkHz) allowing the exposure image data to be refreshed continuously suchthat large areas of a substrate (photosensitive medium) may becontinuously scrolled and dynamically exposed by scanning at highspeeds.

FIGS. 5a-5c illustrate exemplary computer aided design slice patterns ofa turbine airfoil mold, in accordance with an exemplary embodiment ofthe present invention. In other words, the seamless scanningconfiguration of a maskless imaging system for projecting CAD slicepatterns of multiple airfoil molds on a large area is illustrated inFIGS. 5a -5 c.

As described, the optical imaging system 200 may be mounted on an X-Ystage, and is scanned while the SLM sends a sequence of frames. Eachframe, e.g., see exemplary frames in FIGS. 5a-5c , represents a portionof a full pattern, mimicking a mask scanning synchronously with thesubstrate. The SLM is illuminated by a pulsed UV light source 205 whilethe pulses are synchronized to the data stream that configures the SLM.As the optical imaging system 200 scans over the substrate 300, the datasent to the SLM is continuously and synchronously updated, line-by-line,and frame-by-frame, delivering the entire pattern information to thesubstrate 300 during its scanning motion. The SLM operates such that theentire array is reconfigured for each pulse to properly form the correctimage on the substrate. The desired image on the substrate 200 may bedigitized and fed to the SLM as a stream of data in a similar fashion asused in raster-writing systems. The difference between the SLM-basedimaging system and conventional raster-writing methods is that themassively parallel processing power of the SLM is utilized to increasethe data throughput by many orders of magnitude.

Exemplary embodiments integrate layered manufacturing of complexthree-dimensional objects by solid freeform fabrication (SFF) usingphotocurable resins with the fine-feature resolution and high throughputof direct digital computer-to-plate (CtP) lithography techniques fromthe printing industry. These techniques have recently advanced todramatically increased throughput by using SLMs to pattern large-areaphotosensitive plates directly from computer-processed bitmap images formaking print masters. This integration of technologies achieves adisruptive breakthrough in part build speed, size, and featuredefinition over current SFF methods. Exemplary embodiments may providean ability to rapidly manufacture parts or objects that have macro-scaleexterior dimensions (approximately a few centimeters) and micro-scaleinterior features (approximately microns to approximately tens ofmicrons). Furthermore, exemplary embodiments may be well-suited for massproduction of state-of-the-art integral ceramic cored molds for castingturbine airfoils directly from digital information.

Referring back to FIG. 4, it illustrates a perspective view of a systemand method for fabricating three-dimensional objects, in accordance withan exemplary embodiment of the present invention. That is, a LAMP system100 is illustrated in FIG. 4, and illustrates layer-by-layersimultaneous fabrication of several objects—in an exemplary embodimentairfoil mold structures—over a large area.

In operation, light from UV light sources 205 of the optical imagingsystem 200 is conditioned and conveyed through optics. The UV lightsources 205 are conditioned and conveyed through transmissive andreflective optics onto an array of SLMs 225.

The SLM array may receive a real-time video stream of CAD data-slicebitmap images from the control system 400. A process control computer405 of the control system 400 may turn the corresponding pixels in thearray ON or OFF. As described, the light from the ON pixels may bereflected downwards and transmitted into the projection lens system 230.The projection lens 230 may convey highly focused images at the rate ofseveral kilohertz (kHz) corresponding to the ON pixels onto the surface300 of a photosensitive medium in the material build platform 500. Theoptical imaging system 200, including the light source 205, optics 215,SLM array 225, and projection lens 230, may be scanned along the X and Yaxes at high speeds to continuously expose new areas of the resin 300synchronously with images that are continuously refreshed on the SLMarray. When the entire surface area of the resin 300 has been scannedand exposed, the surface of material build platform 500 may be moveddownward along the negative Z-axis by a slice layer thickness, and a newlayer of photocurable material may be swept by a material recoatingsystem 600.

The material recoating system 600—which for illustration purposes isshown as a wire-wound draw-down bar—sweeps uniform thickness layers ofthe photosensitive medium at high speeds across the interior of thematerial build platform 500, without disturbing the previously builtlayers. Once a new layer of the photosensitive medium has been formed,focusing and alignment optics may ensure that the surface of the mediumis at the focal plane of the projection lens, making fine adjustments inthe Z-direction if necessary. Upon completion of this step, the LAMPprocess repeats the cycle of building the next layer and delivering newresin until the entire build is completed.

As shown in FIGS. 4 and 6-7, the system and method for fabricating thethree-dimensional object includes a maskless optical imaging system 200,a container 500 for holding the medium, material recoating system 600,and the control system 400. In an exemplary embodiment, the LAMP system100 may include: (1) a maskless optical imaging system (MOIS) forexposing the patterns into a photosensitive medium; (2) the materialbuild platform (MBP) for layer-by-layer UV curing and freeformfabrication of a three-dimensional object; (3) the material recoatingsystem (MRS) for rapidly coating approximately 25-100 μm uniformthickness layers of the photosensitive medium onto the MBP; and (4) thecontrol system comprising hardware and software interfaces with theMOIS, the MBP, the MRS, and with 3-D CAD data bitmap slices in order toenable a completely automated and synchronized LAMP system.

When the optical imaging system is a maskless optical imaging system orMOIS 200, MOIS 200 may comprise the UV light source, beam homogenizationoptics, mirrors, condenser optics, illumination optics, an array ofSLMs, and the projection lens system. In addition, the MOIS 200 maycomprise a UV light source, transmission and condenser optics, array ofspatial light modulators (SLMs) (e.g., DMDs), projection lens system,and high-precision XY scanning stage. MOIS 200 may utilize scanningexposure with the SLM array having well in excess of a million modulatorelements. The MOIS 200 exploits state-of-the-art SLM 225, such as DMDchips (e.g., from Texas Instruments) with 1024×768 pixels and with anapproximate 10 kHz frame rate. In addition, MOIS 200 exploits extensivesoftware algorithms to coordinate and synchronize the SLM data framesand the position information of the scanning optical imaging system overthe MBP.

MOIS 200 may be mounted on an overhead gantry style precision XY motionstage with sub-micron position resolution for achieving a minimumin-plane feature resolution of at least approximately 15 μm with anerror of approximately ±1.5 μm. The XY motion stage may scan over theentire MBP 500 at high speeds (e.g., approximately several hundred mm/s)to expose different areas of the top surface of the MBP 500 that has anew unexposed layer of the photosensitive medium.

In an exemplary embodiment, the MBP 500 may comprise a container 505that serves as the build volume 510. The MBP 500 may incorporate a buildsubstrate mounted on a high-accuracy z-translation stage for building anobject in layers e.g., 25 micrometer (and larger) thicknesses using thephotosensitive medium. Thinner layers of the photosensitive medium maybe created when the dimensions of a feature of the three-dimensionalobject require so. Similarly, when the dimensions of a feature of thethree-dimensional object are large, thicker layers of the photosensitivemedium may be used. In an exemplary embodiment, the overall dimensionsof the overall build volume 510 may be approximately 24 inches (×) by 24inches (Y) by 16 inches (Z) (24″×24″×16″). A build surface 515 made of aprecision machined plate 516 may be located within the build volume 510(i.e., in the MBP's interior) and may be mounted on a precision linearmotion stage for motion in the Z-direction. During the fabrication of apart, the build surface 515 may be moved incrementally downwards by adistance equal to the layer thickness with which the part is beingbuilt. The control system 400 may control this downward movement.

In an exemplary embodiment, the MBP 500 may be constructed using aprecision linear positioning system with sub-micron resolution forachieving a minimum build layer thickness of approximately 25 μm with anerror of approximately ±2.5 μm. When the entire surface area of the MBP500 has been scanned by the MOIS 200 and the exposure has beencompleted, the build surface 515 may move down via its downwardly movingplate 516, and the MRS 600 may apply a new layer of the photocurableceramic material.

The MRS 600 may comprise a coating device 605, which may be, withoutlimitation, a wire-wound Mayer draw-down bar, a comma bar, or a knifeedge or a slurry dispensing system. The MRS 600 may incorporate acoating device capable of applying coatings as thin as approximately 2.5microns with 0.25 micron variation. The MRS 600 may be designed tosuccessively deposit the layers of the photosensitive medium. During apart build, upon the completion of a layer exposure, the MRS 600 mayquickly sweep the medium across the build area under computer 405control. The MRS 600 may implement principles from the web-coatingindustry, where extremely thin and uniform coatings (on the order of afew micrometers) of various particulate-loaded formulations aredeposited on fixed, flat, or flexible substrates.

In an exemplary embodiment, the photosensitive medium may comprise aconcentrated dispersion of refractory ceramic particles in aphotopolymerizable matrix. The ceramic particles can, after firing,produce a high quality ceramic object. In an exemplary embodiment, thephotopolymerizable matrix may be a mixture of camphor with an acrylicmonomer, formulated so that it is solid at room temperature, but liquidwhen warm (above about 60° C.). Camphene may be selected due to of itsconvenient melting point, and because solid camphene has a high vaporpressure, making it easy to remove by sublimation. Liquefied resin maybe supplied warm to the recoating system, and applied on the materialbuild platform as a thin liquid layer. It may quickly freeze, providinga smooth solid surface. Exposure to the UV may cross-link the monomer,rendering the exposed areas infusible. After building all the layers,heating the block of build material above about 60° C. may melt away theunexposed material, which drains as a liquid. After draining, the solidcamphene c removed from the green body by sublimation at or slightlyabove room temperature. Next, after sublimation the LAMP-fabricated moldmay be a dry body containing enough polyacrylate for high greenstrength, but not so much that special binder-burnout is required beforefiring.

The solid build material may further provide sharper curing profiles,and may improve resolution. A solid build material may not require aliquid vat with associated issues of flow-related disturbance of thepreviously-exposed layers. Consequently, recoating may be done muchfaster and with thinner layers, because the higher shear forces from therecoating device may not disrupt underlying solid layers.

In addition, eliminating liquid flow in a vat enables the build platformto be rapidly translated in the X-Y directions. Consequently, themechanics of the exposure and optical system design are greatlysimplified, improving precision and repeatability.

The solid build material that the support structures are inside may notbe needed. Support structures are endemic to 3-D free-forming fromliquid materials. A layer that has overhangs (such as a curved part)cannot float in space, so the build software produces a temporaryscaffold to support it, i.e., a support structure. After doing aconventional SLA build, the support structures need to be removed. Butif the object is a metal casting mold, the cavity on the inside of themold is the relevant surface, and an interior support structure cannotbe simply removed. Careful consideration of the design is required tofind optimal build directions where support structures are not needed.Solid build materials do not require support structures, because theoverhangs are supported by the solid (but uncured) material below.

Silica is an exemplary ceramic material, whereas the LAMP process may beapplied to a wide range of ceramic materials. Alumina- oryttria-containing photosensitive media may be produced, for example, tocast more reactive superalloys (for making turbine airfoils) thatrequire alumina or yttria molds. Adjusting exposures for thealumina-based or yttria-based resin causes a different sensitivity forphotopolymerization. Sensitivity in ceramic-containing resins is mostlylimited by light scattering, which depends upon the refractive index ofthe ceramic and also on the particle size distribution and suspensionstructure affecting photon transport. The refractive index of silica isclose to the monomer, so silica resins are very sensitive. Alumina andyttria have higher refractive indices and so they require a higherexposure dose.

A new photosensitive medium may be developed taking into account therheological behavior of the medium material in the liquid state, thephotocuring behavior of the medium, the clean draining of the uncuredmedium, cured polymer removal, firing, and the refractory properties ofthe final fired ceramic object.

Development of a solid medium may adopt the successful terpenoid-basedvehicles, such as camphor, which may be removed after forming bysublimation. This eliminates nearly all drying and binder burnoutissues. The rheology of ceramic powders in warm liquid terpenoids iswell understood, and effective colloidal dispersants are commerciallyavailable. Detailed information is available on solidification ofcamphor and camphene at room temperature, as these have been a preferredmodel system for solidification research. The solidification ofconcentrated ceramic suspensions is also well understood. Preliminaryresults of the photopolymerization behavior of solid photosensitivemedium based on terpenoid-acrylate monomers are encouraging. Solidpolymers are routinely used in pre-press platesetting print industry, aswell as in photolithography.

The photocuring characteristics of the ceramic-containing resins as afunction of composition and properties may be tailored to develop anoptimized PCMS composition. Examples of ceramic-containing resins foruse as the photosensitive medium and of their manipulability may befound in U.S. Pat. No. 6,117,612, which is incorporated by referenceherein as if fully set forth below.

The control system 400 may comprise the PCS 405 for the LAMP system 100.In essence, the PCS 405 forms the brains of the LAMP system 400 and isthe central processing unit of the system, responsible for automationfunctions. The PCS 405 may include the software algorithms to conductadaptive slicing of the integral cored mold CAD files for optimizedlayer thickness, part surface finish, avoidance of stairstepping, andminimum build time as a function of critical features and feature sizespresent in the mold design. The PCS 405 further may include thealgorithms and signal communication logic for coordinating the motion ofthe MBP, the MRS, and the MOIS for automated layer-by-layer materialdelivery, scanning, and photoexposure to build 3D parts in the shortestpossible time with the least possible idle time in the LAMP machine.Software algorithms may process the CAD data slices into the stacks ofimages (e.g., see FIG. 10a ) necessary to be flashed to the SLMs at thehigh rates necessary for seamless and maskless exposure of thephotosensitive medium as the MOIS moves at high speeds over the MBP.Software algorithms may also adaptively adjust the exposure dose inreal-time as a function of slice layer thickness to achieve thenecessary full cure depth through the layer thickness regardless of thelayer thickness.

The overall PCS and user interface for the LAMP system that mayintegrate the software algorithms and signal communication logic. ThePCS may include all the necessary CAD data interfaces, machineautomation and control hardware and software interfaces, and faultdetection and recovery in order for the LAMP machine to function as afully automated, operator-free solid freeform fabrication (SFF) machine.For example and not limitation, FIGS. 9a-9e illustrate a plurality ofcross-sectional views of a 3D CAD drawing, and FIG. 10a illustrates aplurality of stacked cross-sectional views of the 3D image that resultsin the turbine airfoil mold 3D casting of FIG. 10 b.

Intelligent adaptive slicing algorithms optimize build speed andthroughput while at the same time carefully accounting for necessaryfeature resolution and/or surface finish embedded in each slice layerthickness. For example, sections of the integral cored mold containingcritical features may be sliced at approximately 25 micron layerthickness, while other regions corresponding to the platform and pourcup with non-critical features or mostly vertical walls may be sliced atapproximately 100 microns or larger layer thickness. Data transfer andfile format protocols transmit the CAD slice data to the SLM array.Intelligent software and hardware algorithms convert the CAD data slicesto the stack of image frames necessary to be flashed at a high refreshrate to the array of SLMs in the MOIS.

FIGS. 6-7 illustrate an exemplary LAMP device illustrating the opticalimaging system, the material recoating system, and the material buildplatform. In other words, FIGS. 6-7 are conceptual schematics of theLAMP system showing the MOIS, the high-precision XY scanning stage, theMRS, and the MBP.

The MOIS 200 is shown in greater detail in FIG. 7. The MOIS 200 maytransform the non-uniform output from the UV light source 205 into arectangular beam of uniform intensity that illuminates the SLM arrayafter being redirected by two mirrors and after passing throughcondenser optics. The SLM array or DMD 225 may be illuminated at anangle with respect to the normal of the pixel plane, because the ONmirrors tilt to direct the light into the projection lens. Theprojection lens 230 magnifies or reduces the image with the appropriateratio and projects the image onto the surface of the medium in the MBP500, which is located at the focal plane of the projection lens. TheMOIS 200 is mounted overhead gantry style on an XY scanning stage and istraversed preferably over the MBP 500, while the SLM sends a sequence offrames. Each frame represents a portion of a full continuously scrollingpattern that covers the entire exposable area of the MBP 500. The SLMmay be illuminated by a pulsed UV light source that is synchronized tothe SLM data stream. As the substrate moves, the data sent to the SLM iscontinuously updated, row-by-row, and frame-by-frame of the micromirrorarray, delivering the entire pattern information to the substrate duringits scanning motion. Considering that there may be between approximately780,000 and 1,300,000 micromirrors on the DMD device, the massivelyparallel processing power of the SLM is utilized to increase thephotopolymerization throughput by at least six orders of magnitude overthat of a single point laser light source, as is the case instereolithography.

Calculations indicate that the exposure time required to photopolymerizethrough the thickness for each slice of a part is on the order aboutfive milliseconds. Commercial high-speed scanning stages may move theoptical imaging system at speeds of 400-600 mm/s, so 200 parts may beexposed in a 24 inches by 24 inches build area within approximately onesecond. A time budget of one second for exposure means that recoating alayer should take no more than four seconds. This means that therecoating device may move at relatively high speeds, upwards ofapproximately 100 mm/s to traverse the 24 inch (610 mm) length of thebuild platform in less than four seconds. The recoating device maysuccessfully coat a new layer of the photosensitive medium at speeds ofapproximately 300 mm/s to approximately 1500 mm/s (approximately 1-5ft/s). These types of coating speeds, commercially in use in theconverting and web coating industry enables the system to meet thecritical time budget per layer, while achieving the high throughoutnecessary to make LAMP a cost-effective process. Calculations furtherreveal that by implementing adaptive slicing to use thinner layers(e.g., approximately 25-75 micrometers) in regions of the partcontaining critical features and thicker layers (e.g., approximately 250micrometers) elsewhere, the part build rate may be increased to at leastapproximately 90 parts per hour, resulting in a cost savings ofapproximately 25-30% per part.

Superalloy objects, e.g., airfoils, are currently cast usingsilica-based shell molds and cores. The photosensitive medium for theintegral cored molds to be produced through the LAMP process may bedesigned and developed based on a silica formulation. A formulation maybe modeled on the same composition used for conventional cores and shellmolds. Using a substantially identical mold composition is helpful foracceptance of superalloy airfoils made by LAMP, because mold chemistrycannot be changed without significant work to re-qualify a component.Silica may be the refractory material because it is relatively easy toremove by leaching after casting. In accordance with an exemplaryembodiment, at least two photocurable ceramic media or materials may beused: 1) a liquid ceramic resin, and 2) a solid ceramic resin.

In a first embodiment, the photocurable ceramic material may be a liquidceramic resin, based on existing stereolithography resins. Such resinscontain approximately 50-60 vol % suspensions of ceramic particles in alow viscosity fluid monomer (non-aqueous acrylate or aqueousmethacrylate). Such formulations are understood and have been wellcharacterized in the art. The liquid ceramic resin is locally solidifiedby photopolymerization where it is exposed to UV light. After the buildis complete, the integral cored mold is a solid ceramic-filledphotopolymer in a vat of liquid resin. The excess resin drains awayafter the mold is removed from the vat. The as-cured mold must undergo abinder burnout process (approximately 200-500° C.) to remove the polymerwithout damaging the mold. Liquid resins, however, have manydisadvantages, including: (1) they cure to a “green” build state that iscomposed of a ceramic in a polymer in the case of acrylate, requiringcareful binder pyrolysis, or a wet ceramic in wet hydrogel (aqueousmethacrylate) which requires careful drying. Both of these arecontrollable for the thin sections relevant for the molds, but place aconstraint on the process; and (2) they require support structures to bebuilt along with the part for some designs.

In a second embodiment, the photocurable ceramic material may be a solidceramic resin including a solid, sublimable monomer solution. This mayinclude a build material that may be applied as a liquid, but one thatfreezes upon application to form a photopolymerizable solid. Forexample, this may be accomplished using a monomer in a molecular solidsolvent. The solid solvent may be a low-melting vehicle that melts aboveabout approximately 50° C. (e.g., a camphor-camphene alloy). In themolten state, it is a fluid suspension of approximately 50-60 vol %ceramic powder in a low viscosity monomer-vehicle solution. A freshlayer of material may be applied as a warm liquid, which freezes afterapplication creating a solid build material. The frozen solid ceramicresin is locally cross-linked by photopolymerization where it is exposedto UV light. After the build is complete, the integral cored mold is asolid ceramic-filled cross-linked photopolymer in a block of frozensolid resin. The block is simply heated above the melting point of thevehicle, so that the uncured excess resin drains away. The remainingcamphor in the as-cured mold is removed by sublimation after building(ambient temperature freeze drying). After sublimation, only a smallamount of cured monomer remains, so binder burnout is much easier.

Camphene is a non-toxic material derived from pine trees (a terpenoid),and melts just above room temperature (50° C.), but is a solid at roomtemperature. Camphor is a similar material, with a higher melting point.These terpenoids may be used for freeze casting of ceramic suspensions.The solid camphene (or camphor) is easily sublimed, so that afterforming it may be removed by sublimation. This eliminates difficultiesassociated with binder polymer pyrolysis (as with polyacrylates) andliquid drying of hydrogels (as with aqueous methacrylates). Thesublimation is a gentle solid-vapor transformation that results in nodimensional change, and hence there is little or no warping or cracking.

Post-processing and firing development efforts may be necessary toachieve functional ceramic devices. The LAMP process may build “green”ceramic devices, including ceramic powder in a photopolymerized binder.Draining the devices of uncured ceramic resin may be necessary, andeffective procedures for draining, flushing, and removal of all loosematerials may further be necessary. After draining is complete, theas-built “green” ceramic devices may be successfully fired for polymerremoval and sintering to create strong objects with the correctmineralogy and functionality.

While reference was made herein to turbine airfoil molds, theembodiments of the present invention have wide-ranging applicationsbeyond turbine airfoils. The embodiments disclosed herein allow for thedesign and manufacture of components that would otherwise be difficultor impossible to manufacture conventionally. With respect toceramic-containing LAMP products, the disclosed embodiments mayradically change how the casting of nearly any component that employstemporary cores and molds is done worldwide.

The various embodiments of the present invention are further illustratedby the following non-limiting example. LAMP was used to build complex 3Dproducts by photo patterning many thin layers of a UV-curable resin. Anexemplary UV-curable resin contains approximately 76 weight percentsilica powder prepared by grinding fused silica to an average particlesize of 7 microns, 19.17 weight percent SR238 monomer (Sartomer,Warrington Pa.) and 2.34 weight percent SR494 monomer (Sartomer,Warrington Pa.), 1.58 weight percent Variquat CC55 dispersant (Degussa),and a photointiator, such as 0.86 weight percent Irgacure 819(Ciba-Giegy). Other photoinitiators, absorbers, or dyes may be added tomodify the UV-curing characteristics as desired. A maskless opticalimaging system scanned the UV-curable resin with a high resolutionbitmap pattern to cure individual layers. Fresh layers were applied, andthe process was repeated to generate complex objects on the order of 10centimeters in size, with internal and external features on the sizescale of about 50 micrometers. Refractory ceramic molds were producedusing as the resin UV-curable suspensions of silica powders in acrylatemonomers.

In one aspect of the present invention, there is a system forfabricating a three-dimensional object. The system includes an opticalimaging system, a photocurable medium, and a control system. The opticalimaging system provides a light source. The photocurable medium changesstates upon exposure to a portion of the light source from the opticalimaging system. The control system controls movement of the opticalimaging system, wherein the optical imaging system moves continuouslyabove the photocurable medium.

In addition, the optical imaging system comprises a reflector receivinga portion of the light source; an optical lens system comprising a lensthat receives a portion of the reflected light source; a spatial lightmodulator for receiving the reflected light source from the optical lenssystem; and a projection lens for focusing the light source receivedfrom the spatial light modulator onto a surface of the photocurablemedium. Alternatively, the optical imaging system includes a masklesslight system for providing the light source and comprising a spatiallight modulator scanning a portion of the medium. In an exemplaryembodiment, the light source continuously changes as the optical lightsystem moves over the surface of the photocurable medium.

The photocurable medium may include a photopolymer. The control systemmay receive a computer aided design drawing.

The optical imaging system projects a two-dimensional image comprising across-section of a three-dimensional object to be formed, thetwo-dimensional image received from the control system, onto a surfaceof the medium. The projected two-dimensional image may be a dynamicimage that continuously changes as the optical imaging system scans overthe medium.

The system further comprises a container for housing the photocurablemedium. The container includes a lower platform that may move downwardlyfor lowering away from the optical imaging system, wherein the containerincludes an inlet for introducing more of the photocurable mediumtherein.

The system further comprises a recoating system for rapidly coating auniform thickness of the photocurable medium.

In another exemplary aspect, an optical modeling method in which aphotocurable medium is exposed with a light beam to form athree-dimensional model includes a number of steps. The method comprisesmoving a maskless optical imaging system providing the light beam in acontinuous sequence; presenting the light beam on a portion of thephotocurable medium; lowering a plate upon which the photocurable mediumresides; and applying a new layer of photocurable media.

The method may further include analyzing a plurality of two-dimensionalcomputer aided designs; the light beam presented on the portion of thephotocurable medium having the shape from one of the plurality oftwo-dimensional computer aided designs. In addition, the method mayfurther include projecting the light beam that continuously changes asthe light beam scans a surface of the photocurable medium. Further, themethod may include providing a material build platform for housing thephotocurable medium and the plate upon which the photocurable mediumresides. The method may include directing the light beam to reflect offa reflector, through at least one lens system, and to a spatial lightmodulator.

The lowering of the plate upon which the photocurable medium residesoccurs after the light beam is presented to the portion of thephotocurable medium.

In another aspect, a method for fabricating a three-dimensional objectcomprises moving a maskless optical imaging system providing a lightsource in a continuous sequence; directing the light source to reflectoff a reflector, through at least one lens system, and into a spatiallight modulator; analyzing a plurality of two-dimensional computer aideddesigns; presenting the light source on a portion of a photocurablemedium contained in a material build platform, the light sourcepresented on the portion of the photocurable medium having a patterncorresponding to one of the plurality of two-dimensional computer aideddesigns; projecting the light source to continuously change as the lightsource scans a surface of the photocurable medium; lowering a platedisposed within the material build platform upon which the photocurablemedium resides, the lowering of the plate upon which the photocurablemedium resides occurring after the light source is presented to theportion of the photocurable medium; and applying a new layer ofphotocurable media to the material build platform.

This disclosure describes Large Area Maskless Photopolymerization (LAMP)technology, which is a layer-based manufacturing technology. LAMPtechnology may be used for the fabrication of integrally-cored ceramicmolds, with complex internal geometries, such as in the investmentcasting of high-pressure turbine blades. Unlike most layer-basedmanufacturing technologies that produce prototype parts in plastic, LAMPmay be applied to produce functional ceramic components that maywithstand the rigors of, for instance, high temperature processesinvolved in the single-crystal casting of turbine blades. In someinstances, the complex internal geometries and the stringentrequirements on the physical properties of the parts to be produced maypose multiple challenges.

This disclosure also describes several data processing schemes for usewith the LAMP technology. STL files, which are meshed approximations ofthe part geometry, are typically used in the additive manufacturing (AM)industry. However, owing to the complex part geometries in LAMP, such anapproximation of the geometry may not be cost effective. Therefore, anerror-tolerant, direct slicing approach using ACIS kernel may be used toslice the native CAD geometry and may output high resolution (1500 dpi)bitmap images of the slice contour. STL file slicing algorithms may beused with the LAMP technology. Furthermore, a suite of post processingalgorithms such as error-checking, part placement, tiling and the likethat work on the slice image data may be used with the LAMP technology.

In addition to the data processing schemes that enable basicfunctionality of the LAMP technology, this disclosure also describesseveral computational schemes to further improve part quality using theLAMP technology, such as a volume deviation-based method for adaptivelyslicing CAD models to alleviate “stairstepping” effects on partsproduced using the LAMP technology and other AM processes in general anda gray-scaling and dithering method applied to the slice images toalleviate the stair-stepping effect, which takes into account theeffects of gray scale factor on the curing characteristics of thematerial system when computing gray scale intensities unlike previousapproaches. This disclosure also describes a method for supportinggeometries that result in unsupported features or “floating islands”during part builds. This method may work on native CAD geometry.Moreover, prior approaches may not be applied to the LAMP technology dueto, for instance, the inability to remove support structures after buildcompletion.

FIG. 11 illustrates one embodiment of a LAMP machine 1100 having agantry-style scanning maskless optical imaging system in accordance withvarious aspects described herein. The LAMP machine 1100 may beconfigured as described by FIG. 11. Further, the LAMP machine 1100 maybe configured to include a material recoating system 1101, an overheadgantry style maskless optical imaging system 1103, a high-precision XYscanning stage 1105, and a material build platform 1107.

FIG. 12 illustrates one embodiment of a scanning maskless opticalimaging system 1200 in accordance with various aspects described herein.The system 1200 may be configured as described by FIG. 12.

FIG. 13 illustrates one embodiment of a scanning maskless opticalimaging system 1300 in accordance with various aspects described herein.The scanning maskless optical imaging system 1300 may be configured asdescribed in FIG. 13. Further, the scanning maskless optical imagingsystem 1300 may be configured to include a UV pixel array flashed fromDMD 1301, a projection lens 1303, a DMD 1305, a condenser 1307, a firstmirror 1309, a second mirror 1311, a UV light source 1313, and a domedreflector 1315.

FIG. 14 illustrates one embodiment of a material build platform (MBP)1400 in accordance with various aspects described herein. The materialbuild platform 1400 may be configured as described in FIG. 14. Further,the material build platform 1400 may be configured to include a dynamiccontainment build tank 1401. In one example, at the start of theprocess, the dynamic containment build tank 1401 may be empty, asdescribed by reference number 1411. At the end of the process, thedynamic containment build tank 1401 may have a part 1403 that iscompleted, as described by reference number 1412. During the process,the build tank 1401 may incrementally grows as each layer is added tothe part 1403, as described by reference numbers 1413 to 1420. In oneexample, each side of the dynamic containment build tank may grow aseach layer is added to the part 1403.

FIGS. 15a-15c illustrate one embodiment of a material recoating system(MRS) 1500 in accordance with various aspects described herein. Thesystem 1500 may be configured as described in FIGS. 15a-15c . The system1500 may be configured to use dispense-on-demand to address, forinstance, in-tank and intra-layer sedimentation.

FIGS. 16a-16c illustrate another embodiment of a material recoatingsystem (MRS) 1600 in accordance with various aspects described herein.The system 1600 may be configured as described in FIGS. 16a-16c .Further, the system 1600 may be configured to use dispense-on-demand toaddress, for instance, in-tank and intra-layer sedimentation.

FIG. 17 illustrates a loss of build precision using a material recoatingsystem having a single-edge recoater. In FIG. 17, the material recoatingsystem having a single-edge recoater may cause starvation or doming,which may result in loss of build precision. In one example, for thefirst about ten (10) to about twenty (2) layers, a blade may haveremoved too much slurry and may form a crater shape in the slurry areaaround a mold. Further, after about forty (40) to about fifty (50)layers, a dome shape of slurry may be formed surrounding the mold parts.This doming problem may get worse as, for instance, more layers areadded, which may cause a build of a part to fail.

FIGS. 18a-18e illustrate one embodiment of a material recoating system1800 having a multiblade recoater in accordance with various aspectsdescribed herein. The system 1800 may be configured as described inFIGS. 18a-18e . Further, the system 1800 may be configured to addressthe starvation and doming issues described in FIG. 17, which mayincrease build precision of a part.

FIGS. 19a-19c illustrate one embodiment of a screen printing-styleinking window pane in accordance with various aspects described herein.The screen printing-style inking window pane 1900 may be configured asdescribed in FIGS. 19a -19 c.

FIGS. 20a-20d illustrate a loss of build precision using a materialrecoating system. In FIGS. 20a-20d , the material recoating system maycause erosion of a surface of a part due to, for instance, a largevolume of uncured liquid. Further, as the material recoating systemsweeps new layers at a high speed, a large trapped volume of uncuredmonomer may erode a surface of a part.

FIGS. 21a and 21b illustrate one embodiment of a method 2100 ofconstructing a conformal lattice in an inter-part space using breaklines in accordance with various aspects as described herein. In FIGS.21a and 21b , the method 2100 may include collectively building a buildblock including tank walls, a part, and a conformal lattice. Further,the method 2100 may include reducing a trapped volume of uncuredmonomer, reducing or eliminating part erosion, reducing starvation ordoming, or the like, resulting in increased build precision of a part.

FIGS. 22a-22h illustrate another embodiment of a method 2200 ofconstructing a conformal lattice in inter-part space using break linesin accordance with various aspects as described herein. In FIGS. 22a-22h, the method 2200 may include collectively building a build blockincluding tank walls, a part, and a conformal lattice. Further, themethod 2100 may include performing a post-build part break-out, whichmay include deconstructing the tank walls or the conformal lattice fromthe build block along the break lines. The method 2100 may includeretrieving the part.

FIGS. 23a-23f illustrate one embodiment of a LAMP machine 2300 inaccordance with various aspects as described herein. The LAMP machine2300 may be configured as described in FIGS. 23a -23 f.

FIGS. 24a and 24b illustrate one embodiment of a method 2400 forcorrecting a gap error in accordance with various aspects describedherein.

FIGS. 25(1)-25(3) illustrate another embodiment of a method 2500 forcorrecting a gap error in accordance with various aspects describedherein.

FIGS. 26(1)-26(4) illustrate one embodiment of a method 2600 ofautomated part layout and scaffolding in accordance with various aspectsdescribed herein.

FIG. 27 illustrates one embodiment of a method 2700 of identifying afloating island in accordance with various aspects as described herein.

FIG. 28 illustrates one embodiment of a method 2800 of identifying amultifunctional support structure in accordance with various aspects asdescribed herein.

FIG. 29 illustrates one embodiment of a method 2900 for screening forshrinkage relief and support structures in accordance with variousaspects as described herein.

FIGS. 30a-30e illustrate another embodiment of a method 3000 forscreening for shrinkage relief and support structures in accordance withvarious aspects as described herein.

FIGS. 31a-31d illustrate another embodiment of a method 3100 forscreening for shrinkage relief and support structures in accordance withvarious aspects as described herein.

FIG. 32 provides a chart 3200 of screening-based grayscale workingcurves for one embodiment of a LAMP system.

FIG. 33 provides a chart 3300 of screening-based grayscale workingcurves for one embodiment of a LAMP system.

FIG. 34 provides a chart 3400 of screening-based grayscale workingcurves for one embodiment of a LAMP system.

FIG. 35 provides a chart 3500 of screening-based grayscale workingcurves for one embodiment of a LAMP system.

FIG. 36 provides a chart 3600 of screening-based grayscale workingcurves for one embodiment of a LAMP system.

FIG. 37 provides a chart 3700 of screening-based grayscale workingcurves for one embodiment of a LAMP system.

The LAMP process may be intended to fabricate high-precision internallycooled turbine blades and hence may not afford the coarse tessellatedgeometry approximation of STL files.

The native CAD geometry may need to be processed to output the slicedata used for building these components. A direct slicing algorithm foraccomplishing this may be implemented using a geometric kernel such asACIS.

FIGS. 38a-38f illustrate one embodiment of a method 3800 of performingdirect slicing in accordance with various aspects as described herein.In FIGS. 38a-38f , the method 3800 may include loading an original CADpart into a program, as referenced at 3800 a. The method 3800 mayinclude computing a bounding box, as referenced at 3800 b. The method3800 may include creating a slice plane, as referenced at 3800 c. Themethod 3800 may include computing an intersection between the part andthe slicing plane, as referenced at 3800 d. The method 3800 may includerasterizing an intersection wire to create a bitmap image, as referencedat 3800 e. The method 3800 may include obtaining or compressing slicebitmaps using, for instance, CCITT FAX4, as referenced at 3800 f. TheACIS kernel is a commercially available C++ CAD library marketed bySpatial Corp, a subsidiary of Dassault Systems. It offers robust APIs(Application Programming Interface) and function calls for most of thebasic CAD operations. These APIs have been integrated into the slicingsoftware to produce CAD slices. The resulting CAD slices are thenrasterized to obtain the bitmaps used for exposure.

The original CAD mold that needs to be sliced may be first loaded intothe algorithm using ACIS's load functions, as referenced at 3800 a. ACISlibraries may work with the SAT file format and hence CAD files in otherformats may need to be converted first into the SAT format either byusing commercial CAD software or by using ACIS's inbuilt file formattranslation functions. During the translation, numerical or topologicalinaccuracies may creep into the part. In severe cases, error checkingand correction schemes may need to be implemented. Once the part hasbeen loaded, its bounding box may be computed to obtain an estimate ofthe size of the bitmaps that would be generated, as referenced at 3800b. A slicing plane may then be created and intersected with the partusing, for instance, ACIS's Boolean APIs to get an intersection wire, asreferenced at 3800 c. Once the intersection wire is obtained, it may berasterized to obtain the bitmaps, as referenced at 3800 d. This mayinvolve shooting rays for each row of pixels in the image and computingthe intersection points with the intersection wire. Pixel values maythen be filled with alternating white and black segments in between eachof these intersection points, as referenced at 3800 e. The bitmap imagesobtained may then be compressed using CCITT fax4 lossless compressionscheme that compresses the data by three orders of magnitude without anyloss, as referenced at 3800 f. CCITT fax4 is an industry standardlossless compression scheme for efficiently compressing 1-bit TIFFimages. These bitmaps may then be fed to the post processing algorithms.

In order to accomplish the tasks discussed in the basic algorithmoutline shown in FIGS. 38a-38f , several different steps may need to becompleted. An example of these steps is shown in the pseudocode fordirect slicing, referred to as Algorithm 1.

Algorithm 1:   1: set ACIS parameters like native resolution   2: setbuild parameters like layer thickness and slice image resolution   3:import CAD File to SAT format using ACIS Interops module   4: performerror checking on part   5: if part free of errors then   6:  getbounding box of the part, i.e., (Xmin; Ymin;Zmin) & (Xmax; Ymax;Zmax)  7:  adjust bounding box dimensions   8:  compute the height and widthof slice image in pixels   9:  create and allocate memory for a‘characterBuffer’ array   10:  for each ‘Z’ location along the builddirection do   11:    create a plane at the specic ‘Z’ location  12:    for each body in the CAD slice do   13:      intersect bodywith the plane created to get a wire graph of the cross-section  14:      store the cross-section wire graph to a ‘crossSectionList’  15:    end for   16:    for each cross-section wire graph in the‘crossSectionList’ do   17:      extract all the edges and store in an‘edgeList’   18:    end for   19:    for each row of pixels in the imagedo   20:      create a ray   21:      for each edge in the ‘edgeList’ do  22:        compute intersection of the edge with the ray  23:        if ray is not tangent to the edge then   24:          storethe intersection point in an ‘intersectionList’   25:        end if  26:        sort points in ‘intersectionList’ w.r.t their ‘X’coordinates   27:        for each intersection point in the‘intersectionList’ do   28:         compute the corresponding pixelnumber in the image   29:         store the pixel number to a‘pixelNumberList’   30:        end for   31:        create temporary‘integerBuffer’ array   32:        for each pixel in the current row ofpixels do   33:          create a boolean variable ‘color’ and initiateto ‘0’   34:          fill ‘integerBuffer’ array with the value of‘color’   35:          toggle ‘color’ value when you hit a number in‘pixelNumberList’   36:        end for   37:        for every 8 valuesin ‘integerBuffer’ array do   38:          compute the decimal sum  39:          identify the corresponding ASCII character  40:          store it in the corresponding row of ‘characterBuffer’array   41:        end for   42:      end for   43:    end for  44:  end for   45:  use ‘characterBuffer’ array information to createthe slice image   46:  save the slice image to a multipage tiff   47:else   48:  display error message to user   49:  exit slicer program  50: end if

After importing the CAD file and performing error checking on the part,it's bounding box may be computed to yield the minimum and maximumextents of the part, i.e., (Xmin; Ymin;Zmin) and (Xmax; Ymax;Zmax). Thesize of the slice image (in pixels) may be determined by these extentsand the resolution (dpi) required. It is a convention in the imageprocessing field to round up the image width to a value that is aninteger multiple of 32 bits (4 bytes) and hence, these bounding boxextents may need to be adjusted. Assuming (without loss of generality)that the build direction is along ‘Z’ axis, the image size may becomputed from these adjusted extents as follows:

$\begin{matrix}{{{{Image}\mspace{14mu} {Width}} = \frac{X_{\max} - X_{\min}}{Resolution}},} & {{Equation}\mspace{14mu} {(1).}} \\{{{{Image}\mspace{14mu} {Height}} = \frac{Y_{\max} - Y_{\min}}{Resolution}},} & {{Equation}\mspace{14mu} {(2).}}\end{matrix}$

Once the image size is determined, an ASCII character array denoted by‘characterBuffer’ may be created and dynamically allocated in order tostore the necessary information for each slice. In binary (black andwhite) bitmap images, each pixel may require 1-bit of memory. There maybe no provision in C++ to access each bit of memory individually. So,sets of values (‘0’s and ‘1’s; ‘0’ denoting black and ‘1’ denotingwhite) of eight pixels may be read at a time and the ASCII charactercorresponding to their decimal sum may be stored in the appropriatelocation of the ‘characterBuffer’ array. After memory has been allocatedfor the image, the part may then be sliced at the corresponding ‘Z’height location by calling the ‘api_planar_slice’ API to produce anintersection contour. Details of the various ACIS APIs may be found attheir documentation portal, as described in ACIS Documentation Portalfound at http://doc.spatial.com/index2.php. If the part file hasmultiple bodies, each of these bodies may be sliced as well and theresulting cross section contours may be stored in a list denoted by‘crossSectionList’. Having computed all of the planar intersections, allthe edges from each of these contours may be extracted and stored in an‘edgeList’. Once the ‘edgeList’ is populated, it may then be time forcomputing the necessary color information for creating the bitmap image.The “exterior” of the part may be denoted by black whereas the“interior” of the part may be denoted by white.

In order to determine if a point is in the interior or exterior of thepart, its membership with respect to the part may need to beestablished, for example, as discussed by Robert B. Tilove, Setmembership classification: A unified approach to geometric intersectionproblems, Computers, IEEE Transactions on, 100(10):874-883, 1980. Apoint's membership with respect to the interior may be established byoriginating a non “osculating” (touch without crossing) curve from thedesired point and letting it propagate to infinity (with the assumptionthat a point infinitely far away is exterior to the part) while countingthe number of times it intersects with the part. If the number ofintersections is odd (even), then the point may be interior (exterior)to the part.

FIG. 39 illustrates one embodiment of a method of identifying the“interior” from the “exterior” in accordance with various aspects asdescribed herein. As may be clearly seen, the ray originating from theexterior point makes an even number (four) of intersections while theray originating from the interior point makes an odd number (five). Itis fairly evident that the same logic applies if the ray were to startat infinity and terminate at a point whose membership is to bedetermined. More importantly, it may be observed that if a ray startingat infinity were to cut across a part, its membership toggles betweeninterior and exterior of the part every time it intersects with the partboundary. For the purposes of making the slice image, this fact may betaken advantage of. Rays starting at the left end of the bounding boxmay be created for each row of pixels in the image and theirintersection points with each of the edges in ‘edgeList’ may becomputed. As previously mentioned, these rays may have to benon-“osculating” for this method to work and hence the computedintersection points may be stored to the ‘intersectionList’ if the rayis non-tangential to the edge with which the intersection point iscomputed. Once the ‘intersectionList’ is created, an ‘integerBuffer’array may be created to store the pixel color data. A boolean ‘color’variable (a variable that may only take values of ‘0’ and ‘1’) may becreated and initiated to ‘0’ to start with (as the start point of theray may be external to the part). The process of marching along the raymay be simulated by counting the pixels as we move from left to right inthe row. The value of the ‘color’ variable may be toggled every time thepixel number exceeds the ‘X’ coordinates of one of the points in‘intersectionList’. This progression along the ray may be counted interms of pixels and may not be counted in the absolute floating-pointdistance traveled along the ray with respect to size of each pixel. Thesize of each pixel may be a floating-point number such as 0.00066667inches for a 1500 dpi image and counting the distance traveled withrespect to this size instead of the integer pixel numbers may lead tofloating point errors and may result in rough edges in the slice image,as described in FIG. 40. FIG. 40 is a slice image having rough edges dueto floating point errors in counting a distance traveled. In FIG. 40,the inset shows the resulting rough edges. Such rough edges may diminishthe surface quality of the part and hence may need to be avoided. Oncethe integer values of pixels are properly filled, the ‘integerBuffer’array may then be converted to the corresponding ASCII characters tofill the ‘characterBuffer’ array for the image. The ‘character-Buffer’array may get completely filled when this process of intersection andcollecting the pixel color information is completed for all the rows ofthe image, at which point it may be used to make the compressed TIFFimage.

FIG. 41 illustrates test parts used in much of the previously reportedwork in the direct slicing literature. As may be seen, most of the testparts are single volume solids with a few that have one or two voids inthem. In comparison, FIG. 42 shows a CAD model of a typical internallycooled HP turbine blade. It is deliberately shown in the wire frame viewto give a better appreciation of the geometric complexity involved.Every edge in the figure represents an interface where two or more NURBSsurfaces meet. Upon comparing the test parts previously shown with theHP blade mold, the order of magnitude difference in the geometriccomplexities involved in LAMP parts is evident. There is so much scopefor errors with parts of such high complexity. Tiny gaps in the modeldue to CAD translations or non manifold geometry due to improperlydefined surface intersections at the interfaces by the designer are verycommon. In order to successfully slice the model, the direct slicingalgorithm described in the previous section may be implemented to betolerant to these errors.

It was observed that errors occur in two steps of the direct slicingalgorithm discussed in the previous section. The first step is slicingwhich involves computation of the intersection between the slice planeand the CAD object. Due to the improperly defined geometry at complexregions of the mold, in some instances the slicing operation fails toproduce a wireframe intersection curve (step (c) in FIG. 10). The secondstep that contributes to errors is rasterization (step (d) in FIG. 10)which involves computing the intersections between rays and the wireframe intersection curve. Any gaps in the model manifest as gaps in thewire frame curve and these, in turn, manifest as stray lines in therasterized image (refer to FIG. 28a for an illustration of these straylines). It was observed that the errors produced in these two steps arevery sensitive to a parameter known as ACIS Resolution which defines howsensitive ACIS kernel is to the inherent topological errors in the CADmodel.

FIG. 43a provides a chart 4300 a of the number of stray lines observedin each image from a stack of hundred consecutive slices produced at twodifferent ACIS resolutions. It may be seen that consistently morenumbers of errors are produced in each slice layer at the lowerresolution (lower ACIS tolerance to topology errors) value. Not onlydoes the ACIS Resolution parameter influence the slice image errors inrasterization, but it was also observed to influence the errors producedin the slicing step. When the slicing operation fails, in some instancesit was observed that by lowering the ACIS resolution (thus making thekernel more tolerant) and re-slicing, the wire frame intersection curvesmay still be computed.

Keeping this fact in mind, in order to tolerantly slice the erroneousCAD geometry, two levels of error tolerance are embedded in the directslicing algorithm. The first is in the CAD space which is aimed toalleviate the problems induced in the slicing step. If the slicingoperation fails, the algorithm dynamically lowers the ACIS resolution totry and compute an intersection curve. If this fails, the slice planelocation is perturbed by a small amount along the the height of the part(usually by ±10 μm) and the slicing operation is conducted again at thisnew slice plane location with various resolutions in order to explorethe possibility of successfully computing a wire frame slice. In extremeinstances, if the slicing operation still fails, the correspondingimages cannot be created, and these are then borrowed from the outputobtained by slicing an STL representation of the same part (STL fileslicing approaches are discussed in Section 2.3).

The second level of error tolerance is in the image space. As waspreviously discussed, having successfully computed the wire frameintersection curve, stray lines may sometimes result in the output sliceimages during to the rasterization step of the direct slicing process.In order to alleviate this problem, an error checking algorithm thatautomatically detects and corrects these stray lines with a stack ofslice images as input is implemented. Note that this error checkingalgorithm may work on a stack of slice images irrespective of whetherthey are produced by the direct slicing algorithm or the several STLfile slicing algorithms. Hence, this second level of error tolerancing,apart from making the direct slicing algorithm error tolerant, makes allthe STL file slicing algorithms error tolerant as well.

A rough estimate of the time complexity of the direct slicing algorithmand the computational times required to slice a few representative partsis given in this section. The time complexity of the algorithm may beestimated as follows: Assuming there are N surfaces in the part, forevery layer in the part:

1) N surface intersections need to be computed with the slicing plane.This amounts to N operations requiring roughly constant time.

2) Next, considering the worst case scenario, for each row of pixels inthe image, N ray-edge intersections need to be computed. This amounts toanother Image Height*N operations.

3) Once the intersection points are computed, the proper integer pixelvalues need to be determined for each pixel in the slice image. Theseneed to be later converted to character values to properly create the1-bit TIFF image. These two operations will together amount to C*ImageHeight*Image Width operations where C is some constant.

So, by adding together the number of operations for each of the stepsdescribed above, we may arrive at the time complexity for the algorithmas shown below:

T(N)=#Layers*[N+Image Height*[N+C*Image Width]],  Equation (3).

Where, N denotes the number of surfaces in the part and C is a constant.The computation time of the algorithm roughly scales linearly with thenumber of layers in the part, which may be directly proportional to theheight of the part and inversely proportional to the Layer thickness,and the number of surfaces in the part. Although the expression inEquation 3 predicts the slicing time to scale quadratically with respectto the Image Height and Image Width, the number of operations are muchmore dependent on the image height than the width of the image.Therefore, the slicing time may roughly scaled linearly with respect tothe image height and may be independent of the image width (linear inreality but with a very small slope) and therefore also scales linearlywith respect to the output resolution (DPI, dots per inch) of the sliceimage. FIG. 43b provides a graph 4300 b of the time to compute one slicescaling with DPI. For the full edged, internally cooled HP turbine blademold shown in FIG. 42, it takes about two (2) minutes to compute eachslice and about a day and a half to compute the entire stack of sliceimages along the length of the part.

Table 1 below provides the computational times taken to compute eachslice for various output image resolutions.

DPI Image Width Image Height Slice Time(s) 300 632 1066 24.963 600 12652132 42.866 900 1898 3199 60.388 1200 2531 4265 80.340 1500 3163 5332100.077 1800 3796 6398 118.458 2100 4429 7465 140.901 2400 5062 8531159.843

Since STL files are typically used in the industry and the directslicing approach using ACIS may not handle these files, severalalternate methods have been investigated.

Reconstructing SAT Files

One of the major weaknesses of the STL file format is the lack oftopological information. As mentioned before, STL files are just arandom collection on triangular facets with no edge or vertexconnectivity information embedded in it. The basic structure of a sampleSTL file is shown below:

solid cube_corner   facet normal 0.0 −1.0 0.0     outer loop      vertex 0.0 0.0 0.0       vertex 1.0 0.0 0.0       vertex 0.0 0.01.0     endloop   endfacet   facet normal 0.0 0.0 −1.0     outer loop      vertex 0.0 0.0 0.0       vertex 0.0 1.0 0.0       vertex 1.0 0.00.0     endloop   endfacet   facet normal 0.0 0.0 −1.0     outer loop      vertex 0.0 0.0 0.0       vertex 0.0 0.0 1.0       vertex 0.0 1.00.0     endloop   endfacet   facet normal 0.577 0.577 0.577     outerloop       vertex 1.0 0.0 0.0       vertex 0.0 1.0 0.0       vertex 0.00.0 1.0     endloop   endfacet endsolid

As may be seen, each of the facets and their respective vertexcoordinates and normal vectors are listed successively in an arbitraryorder. This poses constraints in efficiently performing several vitaloperations on them. First, slicing the model may become difficult andtime consuming. In addition to slicing, performing error checkingoperations like identifying missing facets or gaps in the model,computing integral properties like mass, center of gravity, volume orthe like, which are important for various process planning operationslike part orientation, build area packing or the like, and manipulationof part geometry may become difficult as well. With the ultimateobjective of alleviating these limitations, an algorithm may beimplemented to reverse engineer a CAD file (or a SAT file) from theinput STL file with all the topological information embedded in it.Doing this may aid in using the robust APIs of ACIS to perform theslicing operations and other vital operations like error checking,calculating the integral properties, manipulation of part as previouslystated, or the like. In order to reverse engineer an SAT file, the BRep(Boundary Representation) data structure of ACIS may need to be builtfrom ground up.

FIG. 44 shows the various elements of the BRep (Boundary Representation)data structure. The BRep (Boundary Representation) data structure mayneed to be created and populated. Each body in the BRep data structuremay be divided into ‘Lumps’. Lumps may or may not be disconnected andmay be present for the reason of simplifying the geometry to make theCAD algorithms more efficient. Each Lump may include a list ofdisconnected closed objects called ‘Shells’. Each shell may include alist of ‘Faces’ that bound the space defined by the shell. Each ‘Face’may include a series of ‘Loops’. A Loop may be a ring of end-to-endconnected ‘Co-edges’. A Co-edge may be a topological entity associatedwith every ‘Edge’ in the model and may be used to store edgeconnectivity information in the part. If two faces meet at an edge, thecorresponding co-edges from the loops of each of these faces may referto the same edge and this may be how the modeling kernel identifiesadjacency information between them.

To populate the data structure and create an SAT file from a triangularmesh, the following steps may be performed:

1) For every listed facet, vertices may need to be created. Co-edgesconnecting these vertices may need to be created as well and may belooped in the right ‘sense’ such as clockwise or counter-clockwise.

2) From the face adjacency information, edges may need to be created andcorresponding co-edges from the adjacent faces may need to point to thesame edge.

3) Again, from the face adjacency information, all the interconnectedfaces may need to be grouped into shells. At the end of the grouping,each shell may have a list of all the faces that are interconnected butdo not touch or intersect with any of the faces of the other shells.

4) These shells may be arbitrarily grouped into lumps and the whole bodymay be created from the resulting list of lumps.

To reverse engineer an SAT file, all of the topological information likevertex and edge connectivity and facet adjacency may need to beextracted from the STL file. Special data structures may need to beimplemented to accomplish this.

The Corner table data structure may store the topology and connectivityinformation in two integer arrays. FIGS. 45a-45c illustrate a cornertable data structure 4500 in accordance with various aspects describedherein. In FIGS. 45a-45c , the corner table data structure 4500 may beconfigured to include nomenclature 4500 a or integer arrays 4500 c thathold topology and connectivity information. The region around a vertexin a facet may be loosely referred to as a ‘Corner’. The vertex thatcorresponds to that corner may be referred to as ‘v(c)’. The corneropposite to the current corner ‘c’ may be referred to as ‘o(c)’. Theleft and the right corners may be respectively referred to as ‘l(c)’ and‘r(c)’. The next and previous corners may be given by ‘n(c)’ and ‘p(c)’,respectively (assuming the vertices are listed in a counterclockwisemanner). The triangle to which the current corner belongs may bereferred to as ‘t(c)’. The two integer arrays that store theconnectivity information may be the Vertex array ‘V[c]’ and the Oppositearray ‘O[c]’, as shown in FIGS. 45a-45c . For any given corner ‘c’, thecorresponding vertex and opposite corner indices may be obtained fromthe Vertex array ‘V[c]’ and Opposite array ‘O[c]’, respectively. Oncethese two arrays are populated, the adjacency information may beavailable. For example, starting from a random corner ‘c’, the lefttriangle may be accessed by querying t(o(p(c))), the right triangle byt(o(n(c))) and the opposite triangle by t(o(c)). In order to reconstructan SAT file, the edge connectivity information may also be required.Hence this data structure may be extended by also constructing an edgearray ‘E[c]’. It may store the edge index of the edge opposite to agiven corner ‘c’. If these three arrays are computed, then all thetopological information required to reconstruct the SAT file may berecovered.

FIGS. 46a and 46b show a schematic of a cell structure used to identifyredundant vertices in accordance with various aspects described herein.FIG. 47 is a flow chart of a method 4700 used to fill V[c] in accordancewith various aspects described herein. ‘V[c]’ may be constructed byimplementing a cell structure where the space enclosed in the boundingbox of the part may be divided into discrete cells. As the facets areread from the STL file, each of their vertices may be first checked forredundancy before they are given an index or stored in V[c]. As eachvertex is read, its cell number may be computed. The distance betweenthis vertex, the vertices already present in its cell or the immediateneighboring cells may be computed. If it is less than a set tolerancevalue, then the vertex may be discarded or the index of the vertexclosest to it may be stored in V[c]. If not, a new vertex index may becreated or stored in V[c]. Continuing this process for the vertices ofthe facets in the STL file may result in V[c] being completed.

‘O[c]’ may be constructed by first identifying all the cornersassociated with a vertex and revolving around each vertex, marking theopposite corners. This is done by first populating a temporary datastructure called ‘bins’. Each node in ‘bins’ corresponds to a uniquevertex in the mesh. For each corner ‘c’ in the part, the minimum vertexindex among the vertex indices corresponding to the next and previouscorners of ‘c’ is identified. The triplet of (min{V [n(c), V [p(c)]},max{V[n(c)], V [p(c)]}, c) is stored in the min{V[n(c), V[p(c)]}^(th)node of ‘bins’. This is essentially grouping all the edges originatingfrom the vertex in its corresponding node in ‘bins’ and the corner ‘c’pointing to the edge. After doing this for every corner in the mesh,each node in ‘bins’ will point to all edges originating from a vertexand the corners pointing to those edges. Once ‘bins’ is fully populated,it is easy to check for corners pointing to the same edge originatingfrom the same vertex. If such a pair of corners exits then each corneris marked as the opposite of the other. Doing this for all the edges ineach of the nodes in ‘bins’, ‘O[c]’ may be fully populated. A pseudocode for doing this is shown in Algorithm 2.

Algorithm 2: Constructing O[c]. 1: create and allocate memory for bins2: for each corner c in the mesh do 3:  e1 ← min{V [n(c), V [p(c)]}4:  e2 ← max{V[n(c), V[p(c)]} 5:  bins[e1] ← (e1, e2, c) 6: end for 7:for each node in bins do 8:  for any pair of triplets (e1, e2, c) and(e1′, e2′, c′) 9:  if e1 = e1′ and e2 = e2′ then 10:    O(c) ← c′11:    O(c′) ← c 12:  end if 13: end for

Once ‘V[c]’ and ‘O[c]’ are constructed, ‘E[c]’ may be easily constructedas follows. First an empty array ‘E’ is created and initialized to null.For every corner ‘c’ in the mesh, check if either or both of ‘p(c)’ and‘o(p(c))’ are not pointing to any edge. If one of them is not pointingto an edge, assign the edge index of the edge pointed by the other. Ifboth of them are not pointing to any edge, then create a new index forthe edge corresponding to the two vertices of ‘c’ and ‘n(c)’ and storethis edge index in ‘E[c]’ for the two corners ‘n(c)’ and ‘o(p(c))’.Doing this for every corner in the mesh, the ‘E[c]’ table may be fullypopulated. A pseudo-code for constructing ‘E[c]’ is given in Algorithm3.

Algorithm 3: Constructing E[c]. 1: create and allocate memory for anarray E 2: for each corner c in the mesh do 3:  E[c] ← NULL 4: end for5: edgeIndex ← 0 6: for each corner c in the mesh do 7:  if E[p(c)] =NULL and E[o(p(c)] = NULL then 8:    create a new edge with verticesV(c) and V(n(c)) 9:    E[p(c)] ← edgeIndex 10:    E[o(p(c))] ← edgeIndex11:    edgeIndex ← edgeIndex + 1 12:  else if E[p(c)] = NULL then13:    E[p(c)] ← E[o(p(c))] 14:  else 15:    E[o(p(c))] ← E[p(c)]16:  end if 17: end for

Having constructed V[c], O[c] and E[c], a simple function called ‘swirl’may be implemented in order to identify the number of disjoint shells inthe mesh. First, an array called ‘Shell’ with a length equal to thenumber of facets in the mesh is initiated and set to null. Each node inshell points to the shell number of a facet. For every corner ‘c’ in themesh, if its corresponding facet ‘t(c)’ is not assigned to a shellnumber in ‘Shell[t(c)]’ the number of shells is incremented by one andthe Swirl function is called for the corner ‘c’. Swirl function is arecursive function which calls itself. When it is called for a specificcorner, it first sets the shell number for the facet and calls itself onthe left (‘l(c)’) and right corners (‘r(c)’) of ‘c’. Through thisprocess of calling itself recursively, it tags all the interconnectedfacets with a shell number and this process continues until all thefacets are tagged with a shell number. At the end of the routine, thenumber of disjoint shells in the mesh and the list of facets belongingto each shell may be identified. A pseudo code for doing this is shownin Algorithm 4.

Algorithm 4: Identifying the number of disjoint shells in a mesh using‘Swirl’ function. 1: create and allocate memory for an array ‘shell’ 2:for each facet ‘t’ in the mesh do 3:  shell[t] ← NULL 4: end for 5:#shells ← 0 6: for each corner ‘c’ in the mesh do 7:  if shell[t(c)] =NULL then 8:    swirl(c, #shells) 9:    #shells ← #shells + 1 10:  endif 11: end for 12: function swirl(c, k) 13:  if shell[t(c)] = NULL then14:    shell[t(c)] ← k 15:    swirl(l(c), k) 16:    swirl(r(c), k)17:  end if 18: end function

In this way, once all the arrays ‘V[c]’, ‘O[c]’, ‘E[c]’ are computed andthe number of disjoint shells identified, all the required topologicalinformation for reconstructing a SAT file from the STL mesh isrecovered. Using this information, the SAT file may be constructed bypopulating the BRep data structure as previously discussed. An algorithmwith these ideas has been implemented and STL files were successfullysliced with the ACIS kernel. In addition to slicing, other operationslike error checking, geometry modification, calculation of integralproperties like center of gravity, volume etc. have also beensuccessfully performed.

Although, the approach of recovering the topological information hasseveral advantages as outlined before, it does have its limitations. Oneof the severe limitations crippling this method is the excessive size ofthe resulting SAT files. This is due to the fact that a number of excessentities like edges, coedges, vertices, faces etc need to be created tostore the topological information in place of much fewer entities in thecase of a native CAD representation. For example, if the STL file of asphere consisting of N facets were to be reconstructed into a SAT file,it would now have N surface planar patches and several edges andvertices in place of just the one surface if it was represented in itsnative CAD format. Due to all of these excess entities, the SAT filesize is several times larger than that for a native CAD filerepresenting the same geometry, and this file size scales linearly withthe number of faces. Table 3 below gives an estimate of the SAT filesizes generated for a few sample meshes. FIG. 48 provides a trend ofthis scaling with respect to the number of facets.

TABLE 3 SAT file sizes produced for a few sample STL meshes. # FacetsSAT File Size (KB) 12 12 24 24 540 593 2376 2935 3872 4763 6162 7668

For the complex CAD model of the mold for an internally cooled turbineblade, it is imperative to have an STL mesh of upwards of 5.5 millionfacets. At such large facet counts, this approach may produces largefile slices to work with. Hence, this approach may not be integratedinto the LAMP data processing flow and instead more direct approaches toread and slice STL files have been investigated.

Owing to the huge SAT file sizes being generated using the previousapproach, an algorithm for directly reading and slicing STL fileswithout any intermediate conversions has been implemented. Since an STLfile is a list of facets in random order, a major issue in efficientlyslicing it is the lack of an ability to quickly identify those facetsthat lie in the intersection region from the rest of the facets in thefile. Hence, a data structure of some kind needs to be implemented forthis purpose.

FIG. 49a illustrates a method 4900 a for identifying the intersectingfacets at an arbitrary Z-height in accordance with various aspects asdescribed herein. An example of a triangular mesh and slicing plane isprovided, as referenced at 4901 a. The slicing may be assumed to bealong the z-direction without loss of generality. In order to identifythe intersecting facets, first each facet's maximum and minimumz-coordinates are computed and stored in memory. For a given slicingplane, the facets whose minimum z-coordinate is lesser than the sliceplane height are selected, as referenced at 4903 a. Out of theseselected facets, those whose maximum z-coordinate is greater than theslice plane height may be identified and retained while the rest arediscarded. This way, only those facets that intersect with the givenslicing plane may be isolated from the rest of the facets in the file,as referenced at 4905 a.

In order to do this, a data structure consisting of linked lists isimplemented. FIG. 24 shows a schematic of this data structure. Itconsists of a primary linked list sorted in the increasing order ofz-values. Each node in this linked list consists of its specific z-valueand a pointer to a secondary list that contains all facets with the sameminimum z-coordinate value as the z-value of that node. Once all thefacets in the given STL file are populated in this data structure, it isstraightforward to implement the rest of the operations required toaccomplish the steps of method 4900 a.

For each slice, once the facets in the intersection region areidentified, a simple parametric intersection is computed between thefacets and the slice plane to yield the various edges of theintersection wire. If each of the edges of a facet are represented as astraight line in parametric form as shown in Equation 4 (wheresubscripts ‘i’ & ‘j’ denote two different vertices of a facet), theparameter value at the intersection between the edge and the slice planeat height ‘Z’ may be computed as shown in Equation 5.

$\begin{matrix}{{\begin{bmatrix}x \\y \\z\end{bmatrix} = {\begin{bmatrix}x \\y \\z\end{bmatrix}_{i} + {t\left( {\begin{bmatrix}x \\y \\z\end{bmatrix}_{j} - \begin{bmatrix}x \\y \\z\end{bmatrix}_{i}} \right)}}},} & {{Equation}\mspace{14mu} {(4).}} \\{{t_{z} = \frac{Z - z_{i}}{z_{j} - z_{i}}},} & {{Equation}\mspace{14mu} {(5).}}\end{matrix}$

If the so computed parameter value ‘t_(Z)’ is between ‘0’ and ‘1’, theco-ordinates of the intersection point are computed as shown in Equation6 and stored.

$\begin{matrix}{{\begin{bmatrix}x \\y \\z\end{bmatrix}_{{int}\mspace{14mu} {Point}} = {\begin{bmatrix}x \\y \\z\end{bmatrix}_{i} + {t_{z}\left( {\begin{bmatrix}x \\y \\z\end{bmatrix}_{j} - \begin{bmatrix}x \\y \\z\end{bmatrix}_{i}} \right)}}},} & {{Equation}\mspace{14mu} {(6).}}\end{matrix}$

Each facet yields two intersection points when it intersects with theslice plane. The other intersection point is also computed similarly andthese two points together make an edge of the cross-section wire. Sincethe facets are listed in a random order, the wire edges are alsocomputed in a random order. In conventional contour planning operations,these edges need to be sorted and the intersection loops need to beconstructed. However, for the LAMP process, it is sufficient to generatea bitmap image of the slice. This may be directly accomplished byshooting rays for each row of pixels and computing intersection points.Then, using these points, the pixel values may be filled. In order toefficiently identify the edges that intersect with a particular ray asimilar data structure like the one used for intersecting facets with aslice plane is used, except that these edges are now sorted based ontheir minimum y-coordinates rather than the z-coordinates. Once theedges are identified, the intersection points are computedparametrically in a similar manner as facet-plane intersections werecomputed. The images thus obtained may be saved in CCITT fax4 format andfed to the post-processing algorithms.

The pseudo-code for the algorithm implemented to accomplish the sequenceof operations described in the previous section is shown in Algorithm 5.

Algorithm 5: Direct Slicing of STL files. 1: load STL file of given name2: determine #facets in the file 3: i ← 0 4: zList ← NULL 5: for i <#facets do 6:  bufferFacet ← readFacet(i) 7:  update the max and minbounds of the part 8:  addFacet(bufferFacet, zList) 9: end for 10: usingmax and min bounds, compute image size and allocate memory 11: eList ←NULL 12: for each Z location along the build direction do13:  facetsToSlice ← isolateFacets(zList, Z) 14:  crossSectionWireEdges← slice(facetsToSlic, Z) 15:  addEdge(crossSectionWireEdges; eList)16:  for each row of the image do 17:    Y ← ycoord value correspondingto the row 18:    intersectingEdges ← isolateEdges(eList, y) 19:    foreach edge in intersectingEdges do 20:      create a horizontal ray at Yfrom the left edge of the 21:      bounding box compute intersectionpoints         between ray the edge 22:    end for 23:    computeintegerBuffer from the intersection points 24:    computecharacterBuffer from intBuffer 25:  end for 26:  use information incharacterBuffer to write the slice image to disk 27: end for

To begin with, the STL file of a given name is loaded into the program.STL files may be of two types: ASCII and Binary. ASCII STL files containall the facet information listed in plain text and may be opened in anystandard text editor. Binary STL files store all the information in abinary format instead of plain text and hence may be much smaller insize. Since the typical STL meshes encountered in LAMP have very largefacet counts (upwards of 5 million), the slicing algorithm has beenimplemented to specifically slice binary STL files.

Binary STL files begin with an 80 byte block of memory known as theheader which contains any file specific information. Following the 80byte block, there is a block of 4 bytes which contains the number offacets in an unsigned integer format. Following the first 84 bytes ofmemory in the file, each facet information is stored in blocks of 50bytes. Every facet block of 50 bytes consists of 12 bytes to store thenormal vector (4 each for the three direction cosines) and 36 bytes tostore each of the three vertices. The rest of the 2 bytes of the 50 byteblock for each facet is usually empty but may be used to store specialattribute information like color in some applications.

Once the STL file is loaded into the program, the number of facets inthe file is read from the 4 byte block of memory following the headerand assigned to #facets. Starting from zero, for every i<#facets, thenormal vector and vertex coordinate information of the correspondingfacet is read using the function readFacet and stored in a temporaryvariable called bufferFacet. The pseudo code for the function readFacetis shown in Algorithm 6.

Algorithm 6: Reading a facet from binary STL file. 1: bufferFacet ← NULL2: function readFacet(i) 3:  facetStartLocation 84 + 50 _i4:  bufferFacet:Nx ← readByte(facetStartLocation) 5:  bufferFacet:Ny ←readByte(facetStartLocation + 4) 6:  bufferFacet:Nz ←readByte(facetStartLocation + 8) 7:  for n := 0 to 2 do8:    bufferFacet:V       [i ]x ← readByte(facetStartLocation + 12 +12 * n) 9:    bufferFacet:V       [i ]y readByte(facetStartLocation +12 + 12 * n + 4) 10:    bufferFacet:V       [i ]z ←readByte(facetStartLocation + 12 + 12 * n + 8) 11:  end for 12:  returnbufferFacet 13: end function

This function, in essence, may seek the file to the correct memorylocation corresponding to the i^(th) facet and may read thecorresponding bytes of information within each facet block of memory andmay populate the temporary variable bufferFacet. Each facet i begins atthe (84+50*i)^(th) byte from the beginning of the file as there areeighty (80) bytes for the header, four (4) bytes for #facets and fifty(50) bytes for each of the i−1 facets before the i^(th) facet. Once thefacet starting location is identified and assigned tofacetStartLocation, the rest of the operations may read thecorresponding bytes of information using the function readByte and thex, y, z coordinates of the normal vector and each of the vertices arepopulated.

In this manner, having read a facet from the file, the next step inAlgorithm 5 may be to update the min and max bounds of the part and topopulate the facet in the data structure shown in FIG. 49b . FIG. 49billustrates a data structure used for direct slicing of STL files inaccordance with various aspects as described herein. This isaccomplished by passing each facet that is read from the file to thefunction addFacet.

The pseudo code for this function is shown in Algorithm 7.

Algorithm 7: Populating a facet in the Data Structure. 1: functionaddFacet(facet , zList) 2:  traverse through zList 3:  look for matchingzList node corresponding to facet.minZ 4:  if found then 5:    add facetto the list pointed by the matching zList node 6:  else 7:    create anew node toAdd 8:    toAdd:Z ← facet:minZ 9:    toAdd:facetList ← facet10:    add toAdd to the zList in the proper sorted location 11:  end if12: end function

The given facet's minimum Z-coordinate value is identified and the zListis traversed to find a node whose Z value matches the minimumZ-coordinate of the facet. If such a node is found, the given facet isadded to the list pointed by the node. In the event that such a node isnot found, a new node variable denoted by toad is created with its Zvalue equal to the facet's minimum Z-coordinate and with its facet listpointing to the give facet. This new node is then added to the zList inthe appropriate location so it stays sorted in the increasing order withrespect to the Z values of the nodes.

With the aid of these two functions readFacet and addFacet, by the endof the first loop in Algorithm 5, the min and max bounds of the partwould be determined and the data structure of facets discussed in FIG.49b would be populated. The next loop then makes use of the datastructure thus populated in order to slice the model and output theimages. For a give Z location of the slice plane, first the facetsfalling in the intersection zone of the plane are identified using thefunction isolateFacets and stored in the list facetsToSlice. The pseudocode for isolating the facets is shown in Algorithm 8.

Algorithm 8: Isolating facets in the intersection zone. 1: functionisolateFacets(zList , Z) 2:  facetsToSlice ← NULL 3:  for each node inzList do 4:    if z value of the node is less than Z then5:      traverse through each facet in the facet list pointed 6:      bythe node look for         facets whose maxZ > Z 7:      if such a facetfound then 8:        add facet to facetsToSlice 9:      end if10:    else 11:      break 12:    end if 13:  end for 14: end function

As may be seen from the pseudo code, in order to isolate the requiredfacets to intersect, first each node in zList is read. If the Z valuecorresponding to the node is less than the Z height of the slice plane,each of the facets in the facet list pointed by the node is parsed. If afacet with maximum Z value of greater than the slice plane height isfound, it is added to facetsToSlice list. After each of the nodes whoseZ values are less than the slice plane height have been parsed in thismanner, the isolateFacets function returns back the facets collected infacetsToSlice. Having isolated the facets in the intersection zone ofthe slice plane, Algorithm 5 then computes the intersection of thesefacets with the slice plane using the function slice. Theseintersections are computed parametrically as described in the previoussection. Having computed the intersection edges, which form the contourof the part cross-section, the next step is to generate an image fromthem. In order to accomplish this, rays are created for each row of theimage and their intersection with the contour edges are computed. Inorder to compute these intersections efficiently, the edges are in turnpopulated in a data structure very similar to the one used forpopulating the facets. The edges are arranged into bins based on theirminimum Y-coordinate instead of the Z-coordinate in case of the facets.This data structure for sorting edges is denoted by eList is Algorithm5. The function addEdge is used to populate the edges in this datastructure and its implementation is very similar to addFacet functionpreviously described. After eList is populated, the process of computingintersections between the rays and the edges is the same as the one usedfor computing intersections between the slice plane and facets. For eachray, the intersecting edges are isolated using isolateEdges whoseimplementation is similar to isolateFacets. Once the intersecting edgesare identified, the intersection points are computed parametrically.After the intersection points are computed, the process of creatingbitmap data is performed. First, a temporary intergerBuffer array ispopulated and later converted to ASCII character array charBuffer whichis then used to save the bitmap image.

A rough estimate of the time complexity and the time it takes to finishthe slicing operations is given in this section. If N denotes the numberof facets in an STL mesh, in order to populate the slicing datastructure discussed in the previous sections, the following operationsneed to be completed for every facet read: 1) Scan through the each nodein zList to identify a matching node and 2) Scan through to the end ofthe facet list pointed by the matching node to add the facet. Each ofthese two operations take, in the worst case scenario, N time steps.Since these two operations need to be performed for every facet in thefile, the time complexity for populating the data structure is O(N3).

Polynomial time complexities like N3 are usually acceptable but if the Nin consideration is large, the computational time becomes excessivelylong. A rough estimate of the computational time for slicing STL filesof various mesh sizes using this algorithm is shown in Table 4. FIG. 49cillustrates computational time scaling with respect to a number offacets.

TABLE 4 Slicing time for various mesh sizes. Indexing Time (sec.)Indexing Time (sec.) 81080 11.475 102268 17.902 114818 22.356 16029644.893 191172 68.579 219584 109.218 337128 613.151

As may be seen, for a file with large number of facets, the slicing timeruns into several days. In the case of LAMP, because of the geometriccomplexity of integrally cored HP turbine blade molds, the mesh sizes ofthe STL files go upwards of 5.5M. For such a huge file, it takes morethan 4 days to slice which is prohibitively large. Hence a new STLslicing algorithm is implemented to cut down the slicing time. Detailsof this algorithm and the new data structure implemented are given inthe next section.

Since, for large STL meshes, it takes excessively long to populate thedata structure described in the previous section, a new approach isinvestigated in order to cut down the slicing time. Upon closeexamination, it is evident that the key pieces of information in orderto create the slice images, are the points of intersection of the rayswith the cross-section wire edges. So instead of spending significantcompute time in populating the facets in the previously described datastructure, it sufices to compute and store these intersection points aseach facet is read from the file. Additionally, if these facets arestored in an array structure rather than in linked lists as waspreviously done, data access may be much quicker as arrays have O(1)complexity for indexing and searching while linked lists which have O(N)complexity for the same (i.e, random access vs sequential access). FIG.50 illustrates a data structure 5000 used to store these intersectionpoints in accordance with various aspects as described herein.

Each row in the data structure represents a Z height corresponding toeach slice i in the part. Each column represents a Y level correspondingto a row j of the slice image. Each location (i; j) in the datastructure contains all the intersection points corresponding to the jthrow of the ith slice image.

As each facet is read from the file, depending on its maximum andminimum Z extents, it is possible to determine all the slice numbersthat this particular facet will contribute edges to. For each of theseedges corresponding to each of these slice numbers, it is also possibleto determine all the rows of the respective slice images they contributeintersection points to. Based on this information, as every facet isread, all the intersection points contributed by this facet to each ofthe slices are computed and stored in the corresponding locations in thedata structure shown in FIG. 50. Once the intersection pointscontributed by all the facets in the file are computed and stored, sliceimages may be prepared by using a similar procedure as discussed in theprevious sections.

The pseudo code for implementing this new algorithm for slicing STLfiles is shown in Algorithm 9. The bounding box coordinates of the partare first created, either by doing a linear scan of the whole part or bydirectly inputing the information in the program from the CAD model. Theminimum and maximum vertices of the bounding box are denoted by (minx,minY, minZ) and (maxX, maxY, maxZ) respectively. Next, memory for the 2Darray data structure denoted by zY Matrix is allocated and initiated toNULL. As each facet f is read from the file, the range of slices thatthis facet f contributes edges to is computed. minLayer and maxLayerdenote the layer numbers of the lowermost and uppermost slices in thisrange. For each slice i starting from minLayer to maxLayer, the facet issliced at the corresponding slice height and the resulting edge isstored in a variable denoted by e. For each edge e, the range of imagerows to which this edge contributes an intersection point are computed.The lowermost and uppermost rows of this range are denoted by minRow andmaxRow respectively. For each row j between minRow and maxRow, theintersection point of the edge e and the ray corresponding to the row jis computed and stored in a variable denoted by intPoint. Theseintersections of the facet with the slice plane and the edge with theray are computed parametrically as described in the previous section.The intPoint thus computed is populated in the (i, j)^(th) cell of the2D array zYMatrix. Once this zYMatrix is completely populated after onelinear scan of all the facets in the list, the slice images may becreated. For each slice image i, in order to compute the pixelinformation for each row j, the variables integerBuffer andcharacterBuffer are populated based on the intersection points retrievedfrom (i, j)^(th) cell of zYMatrix. Once the characterBuffer array iscompletely filled for all rows of the slice, it may be used to write theslice image to disk.

Algorithm 9 Improved direct slicing of STL files 1: compute bounding boxof the part 2: (minX; minY; minZ) ← minimum extents of the part 3:(maxX; maxY; maxZ) ← maximum extents of the part 4: zYMatrix ← NULL 5:for each facet f in the file do 6: bufferFacet ← readFacet(f)   7:$\left. {minLayer}\leftarrow{{{floor}\left( \frac{{{bufferFacet}.{minZ}} - {minZ}}{LayerThickness} \right)} + 1} \right.$  8:$\left. {maxLayer}\leftarrow{{floor}\left( \frac{{{bufferFacet}.{maxZ}} - {maxZ}}{LayerThickness} \right)} \right.$9: for each slice i; i := minLayer to maxLayer do 10:   e ←sliceFacet(bufferFacet, i )   11:  $\left. {minRow}\leftarrow{{{floor}\left( \frac{{maxY} - {e.{maxY}}}{pixelSize} \right)} + 1} \right.$  12:  $\left. {maxRow}\leftarrow{{floor}\left( \frac{{maxY} - {e.{minY}}}{pixelSize} \right)} \right.$13:   for j := minRow to maxRow do 14:     intPoint  intersectEdge(e; j)15:     zYMatrix[i ][j ] intPoint 16:   end for 17: end for 18: end for19: for each slice i; i := 0 to #Layers do 20: for each row j; j := 0 toimageHeight do 21:   intPoints ← zYMatrix[i ][j ] 22:   computeintegerBuffer using intPoints 23:   compute characterBuffer usingintegerBuffer 24: end for 25: use information in characterBuffer towrite the slice image to disk 26: end for

A rough estimate of the time complexity and the computational time takento slice STL files using this algorithm is given here. In order to indexall the intersection points in the 2D matrix, it would take N*Z*Y*Coperations, where N denotes the number of facets in the file, Z denotesthe slice range (maxLayer-minLayer), Y denotes the row range(maxRow-minRow), and C denotes some independent constant. In the worstcase scenario, Z and Y may both be equal to N and the time complexityreduces to O(N³) just like the linked list STL slicing algorithmdiscussed in the previous section. However, in typical scenarios, both Zand Y are much smaller than N. The constant C is also very small sincean array structure is used instead of a linked list. Hence, in mosttypical scenarios, the algorithm behaves like it is O(N) complexity witha very small constant value and hence is much faster than the linkedlist algorithm discussed in the previous section. An estimate ofindexing times using this 2D Matrix approach to slice typical STL fileswith various facet counts and the corresponding times for the linkedlist algorithm discussed in the previous section are shown in Table 5.

TABLE 5 Slicing time for various mesh sizes. Indexing Time for IndexingTime for # Facets Linked Lists(s) 2D Matrix 81080 11.475 14.147 10226817.902 14.197 114818 22.356 14.550 160296 44.893 15.466 191172 68.57916.157 219584 109.218 16.895 337128 613.151 18.690 438434 1464.20619.715 531370 2476.122 21.754 678358 4656.452 24.045 756446 6075.47424.921

FIG. 51 illustrates slicing time scaling with respect to mesh size.

As may be seen, the savings in slicing time are substantial using thisapproach. It takes just 30 minutes to slice a 5.5M facet STL file versusthe 4 days it to slice the same file using the linked list approach.This leads to enormous time savings in preparing build ready images foreach new part design.

Although, this new approach reduces the computational time, it does haveits limitations. Firstly, since the facets are just read once anddiscarded from memory, once the slice thickness and image resolution areset, it is impossible to change them dynamically during the execution asthe facet information cannot be retrieved. In the linked list approach,since all the facets are indexed in the data structure, there is alwaysflexibility to change the layer height and image resolution dynamicallyfor applications like adaptive slicing. However, this shortcoming may bealleviated in other ways. Since the slicing time itself is very short,multiple stacks of slice images may be created at multiple layerthicknesses and the proper images from each of these stacks may beselected for utilizing variable layer thicknesses in applications likeadaptive slicing.

Secondly, this new approach uses far more memory than the linked listapproach since it stores all the intersection points of all the rayswith each of the slices in the part whereas in the linked list approach,just the facets are stored in memory. As an example, for the 5.5Mtriangle part, the new approach takes about 2.5 gigabytes of memoryversus just 300 megabytes of memory using the linked list approach.Since memory is very cheap in recent times, this limitation is not asignificant hurdle. Hence, considering the pros and cons of each of theapproaches of STL slicing discussed in this section, the approach inthis section is the preferred method to slice extremely high resolutionSTL files for LAMP.

The slice images produced through STL slicing and Direct CAD Slicing inparticular require further post-processing before they are ready for usein a LAMP build. The details of these various post-processing operationsand algorithms are given in this section.

One of the mandatory post-processing operations that needs to beperformed on the slice images is checking for errors and validity of theimages. These errors are caused by gaps that creep into the model eitherdue to errors in the CAD model or due to translation between differentCAD formats. During the slicing operation, in the process of creatingthe slice images, rays are created for each row of the image to identifythe correct pixel color values as previously described. Any ray thatcoincides with one of these gaps that creep into the CAD model willresult in the omission of an intersection point that should have beencomputed in an error-free file. This omission will result in the pixelcolor value not toggling at the corresponding location and this will inturn manifest as a stray line in the slice image. FIGS. 52a and 52billustrate a particularly bad instance of stray line errors. Such straylines need to detected and corrected before the images may be used forpart builds on the LAMP machine. For this purpose, an error checking andcorrection algorithm has been implemented. The algorithm takes anerroneous slice like the one shown in FIG. 52a referenced at 5200 a andoutputs a corrected slice shown in FIG. 52b referenced at 5200 b.

In order to identify these stray lines, the algorithm scans through eachrow of the image and checks for pixels that are sandwiched by pixels ofan opposite color, i.e, pixels that have a different color value thanthe ones present on the rows immediately above and below the current rowthat is being searched. Once it finds such pixels, it flips their valuesto match the color values of the top and bottom rows to correct thestray lines. This approach works for correcting only stray lines thatare 1-pixel thick but may be extended to detect lines that multiplepixels wide. The details of the extended algorithm along with the pseudocode for detecting stray lines that are multiple pixels wide is givennext.

The pseudo code for the error correction operation is shown in Algorithm10. The given stack of slice images that need to checked are firstloaded into the program. As each image in read from the stack, its pixeldata is first converted from ASCII representation to integerrepresentation for easy data manipulation and stored in an integer arrayintegerBuffer. If an intersection point was missed in the slicingoperation and a stray line caused, then the last pixel of the rowcontaining the stray line will have a white pixel on a surrounding blackbackdrop. This fact is exploited in identifying erroneous rows that needto be corrected. This is accomplished by checking for pixels with acolor value of 1 (i.e, white) in the last column of pixels inintegerBuffer. If such a white colored pixel is identified, it meansthat the corresponding row needs to be corrected for a stray line.Having identified the row at which a stray line occurs, the next step isto determine the width this stray line. So, having identified the row atwhich a stray line originates, the color values of end pixels in therows immediately following the identified row are checked. Ifconsecutive rows are found to have white pixel values, then the width ofthe stray line is more than one. The number of consecutive rows arecounted and the stored in the variable width. Having identified thebeginning row number and the width of a stray line, this information isthen passed to the function correctRow.

Algorithm 10 Error Checking Algorithm.   1: load the stack of images tocorrect   2: for each image in the stack do   3:  characterBuffer ←pixel data of the image   4:  integerBuffer ← convert ASCII data incharacterBuffer to integer data   5:  for each row j of the image do  6:    width ← 0   7:    if the last pixel of row j in integerBuffer =1 (i.e. white) then   8:      width ← width + 1   9:      j ← j + 1  10:      while last pixel of row j in integerBuffer = 1 do  11:        width ← width + 1   12:        j ← j + 1   13:      endwhile   14:      correctedIntegerBuffer ← correctRow(integerBuffer, j −width, width)   15:    end if   16:  end for  17:  correctedCharacterBuffer ← convert correctedIntegerBuffer toASCII data   18:  output the corrected image to disk usingcorrectedCharacterBuffer   19: end for

The pseudo code for the function correctRow is shown in Algorithm 11. Itis just an extended version of the logic described previously forcorrecting one pixel wide stray lines. Three counters i, j and k areused in the algorithm. Counter k keeps track of the row number in theimage corresponding to each row in a multi-pixel wide stray line that isbeing corrected. Counter i keeps track of the number of rows above aparticular row in the stray line that needs to be checked for colorinformation. Similarly, counter j keeps track of the number of rowsbelow a particular row in the stray line that needs to be checked forcolor information. For each pixel in each row of the stray line, thecolor of the corresponding pixel in the row that is i rows above and jrows below is checked. If it is the same but different from the color ofthe current pixel in the row that is being corrected, the pixel value isflipped.

Algorithm 11 row correction function. 1: functioncorrectRow(integerBuffer, row, width) 2:  for i := 1 to width do 3:    j= width − i + 1 4:    k = row + i − 1 5:    for each pixel in row k do6:      if color i rows up = color j rows down ≠ color on current7:        row then flip the current pixel color 8:      end if 9:    endfor 10:  end for 11: end function

For example, lets assume the beginning row number of a stray line isthirty (i.e, row=30). Lets also assume that the width of the stray lineis three (i.e, width=3). Hence in this example, if we were correctingthe first row in the stray line (first iteration of the loop), the colorvalues of the pixels one row above three rows below should be checkedfor equality and if they are equal but different from the color value ofpixels in the first row that is being corrected, then the pixel colorvalue needs to be flipped. The counter values are correspondingly set,i.e, for the first iteration (correcting first row in the stray line),k=30 (beginning row number of the stray line), i=1 (one row above) andj=3 (three rows below). Similarly for correcting the second row in thestray line (k=31), the pixel values two rows (i=2) above and two rowsbelow (j=2) need to be checked for color information and so on.

All of these error checking operations are based on the assumption thatthe collective width of these consecutive stray lines is much less thanthe minimum feature size in the CAD part that is to be sliced. For theblade designs that are currently being built by LAMP have minimumfeatures sizes of about 500 microns, i.e, approximately 30 pixels insize at 1500 dpi. The widest stray lines observed in the slices werefive pixels wide which is much less than the minimum feature size of 30pixels and hence may be corrected with reasonable accuracy.

The other limitation of this algorithm is that, when the stray lines aretoo wide, the corrected rows do not conform to the boundaries of thepart where the color toggles from black to white or vice versa. Theedges of the part in the corrected rows become vertical instead ofsmoothly connecting with the rest of the contour. FIGS. 53a-53cillustrate a method 5300 of rectifying multi-pixel wide rows with straylines in accordance with various aspects as described herein. Thisphenomenon is shown in FIG. 53b referenced at 5300 b for a sample strayline shown in FIG. 53a referenced at 5300 a. When the stray lines arethin (less than 5 pixels wide) the inaccuracy caused is negligible butas they get wider, it needs to be corrected for. This problem may befixed by constructing a spline (a Hermite cubic spline with C1continuity for example) to close the contour in a continuous way and thecolor toggling points in each of the rows in the stray line may becomputed from the so constructed spline. This way smoothness of the edgecontours may be maintained as shown in FIG. 53c referenced at 5300 cwhile correcting stray lines that are arbitrarily wide. Although, it maycorrect a stray line of any arbitrary width, if the stray line is toowide (width of the stray line approaching minimum feature size in thepart) then rather than passively correcting it in the image, thegeometry of the original CAD part needs to be repaired for accurateslices.

In this way, the function correctRow may correct stray lines given thestarting row number of the stray line in the slice image and its width.Returning back to Algorithm 10, once all the stray lines identified inthe integer data of the slice image (integerBuffer) are corrected, it isthen converted back to ASCII data and saved back to disk. In this way,all the slice images in the stack are checked and corrected for errorsand by the end, a stack of error free images are obtained which aretaken through other post processing operations as described in thefollowing sections.

The corrected images as obtained above then need to be tiled properly onan image template for proper part placement in the build area. FIGS.54a-54c illustrate illustrates a method 5400 of tiling in accordancewith various aspects as described herein. FIG. 54a reference at 5400 ashows a typical input image to the tiling code. A mesh structure asshown in FIG. 54b reference at 5400 b is used as the background on whichthis input slice is tiled. The mesh structure has been optimized afterconsiderable experimentation to prevent the uncured Suspension in theempty regions from sloshing around in the build tank during recoating ofa fresh layer of Suspension by the blade. The algorithm automaticallycomputes the maximum extents of the slice image, determines the numberof parts that may be built within the build area, lays them out at thecorrect coordinates and creates break lines along the mesh structure foreasy removal of parts after the build is complete. The final build-readyimages produced by the code look like the one shown in FIG. 54creference at 5400 c. The code runs through the entire stack of the sliceimages to produce a build-ready stack that is then fed to the LAMPmachine.

Depending on the level of complexity of the CAD model, slicing andprocessing the stack of build images may take a substantial amount oftime. For turbine mold geometry, it currently takes two days to preparethe data. Sometimes, during evaluation of various CAD designs, therearises a need to build several designs with minor differences in thefeatures. In such cases, it would be beneficial to implement algorithmsthat may take a base design and implement the minor feature additionsand modifications directly at the image level to generate the buildimages for each of the intended CAD configurations. This would saveenormous amounts of time and effort as it avoids re-slicing the entireCAD model. Such algorithms are currently under development onneed-by-need basis.

A detailed overview of the various data processing algorithms developedfor enabling the basic functionality of the LAMP process was given inthis chapter. The algorithms presented belong to two categories: slicingand post-processing. A brief summary of the work presented in thischapter is given in this section.

Owing to the geometric complexity of the parts encountered in the LAMPprocess, a direct slicing approach using the ACIS kernel was implementedto slice the native CAD geometry instead of the conventional STL slicingapproach ubiquitously used in the additive manufacturing industry. Priordirect slicing approaches presented in the literature tout directslicing to be the cure for all ills posed by STL files. Direct slicingis claimed to be error free and fast while STL slicing is claimed to beprone with errors and time consuming. It was shown in this chapter thatthis claim is only true while working with simple geometries as is thecase with much of the previously reported work. When the geometries arecomplex, direct slicing approach produces more errors and consumes moretime than STL file slicing. The direct slicing algorithm presented inthis chapter is tolerant to such errors.

Although direct slicing approach is the preferred method to produceslice data for the LAMP process, STL file slicing algorithms were alsoimplemented owing to the prevalence of this file format. Multipleapproaches to slice files of this format were implemented. The STLslicing approach using POVRAY, a graphics rendering engine, was easy toimplement but not accurate enough for the purposes of LAMP. An approachto reconstruct topology information from an STL mesh using an extendedversion of the corner table data structure was implemented. However, forcomplex parts like the ones built in LAMP, the SAT files sizes resultingfrom this method proved to be too large to handle. Therefore, a moredirect approach of reading the facet data and sorting it into datastructures similar to the ones reported in literature was implemented.While these data structures yielded reasonably quick slicing times forsmall parts, for high facet counts of the order of 5.5M that istypically required for the LAMP process, they take too long to process(4 or more days). Thus a much faster approach which bypasses the facetdata sorting operation is implemented and found to reduce the processingtime by several orders of magnitude (from 4 or more days to about anhour).

Following the slicing operations, the output data needs to furtherprocessed before it is ready for LAMP builds. For this purpose, severalpost processing like error checking, part placement and tiling, imagelevel geometry modification etc. were implemented and the details ofthese were presented. In summary, the work presented in this chapterestablishes the basic data processing flow required to producesuccessful builds using the LAMP process.

A new volume deviation based adaptive slicing method for BRep models isdeveloped in this thesis. BRep stands for Boundary Representation, akind of data structure widely used for storing CAD model data. The ACISmodeling kernel used for implementing the direct slicing algorithm usesthe BRep format and so do many commercially available CAD softwarespackages like Solidworks, Pro/Engineer, CATIA, Unigraphicx etc. Themotivation for this approach and the details of the algorithm arepresented in this section.

Although several adaptive slicing approaches have been presented in theliterature as discussed in the previous section, there are somelimitations especially in the case of adaptively slicing BRep models.The mostly widely used approach of maximum cusp height criteria foradaptive slicing works well for STL files due to the simplicity of facetdata. However, it becomes extremely complicated and computationallyintensive when implemented for slicing direct CAD models. Forcalculating the cusp height for each layer, a complex optimizationscheme is implemented which involves calculating the vertical normalcurvature at each point in the slice contour (which in itself needsseveral complicated calculations of local tangent and normal vectors)and these computations take a long time. Moreover, the approach onlyworks for parametric surface patches like B-spline and NURBS and arehence not readily extensible to generic BRep CAD models which aredefined by a mixture of parametric splines and analytic curves.

Another approach presented in the literature for adaptively slicing CADmodels uses an area deviation approach. This approach, while being muchmore simple than the cusp height approach for CAD models, is fraughtwith difficulties as it does not consider the local surface geometry ofthe part. It leads to situations where the actual geometric deviation ofthe additive manufactured part with respect to the original CAD geometryis not properly estimated as shown by the example in FIG. 55. FIG. 55illustrates the staircase effect while two created contours are samesize in inner area. As shown in FIG. 55, if the CAD geometry were aninclined cylinder, there would still be a staircase effect in thelayered part while having slice contours of exactly the same area. Insuch a situation, the area deviation approach would fail to identify thegeometry deviation due to staircase effect and hence layer heightadaptation will not be achieved.

The other major approach presented in the literature for adaptivelyslicing CAD models uses a maximum bound on the surface roughnessparameter Ra. This approach is also simple to implement as a closed formexpression relating the layer thickness to the surface roughness Ra fordetermining the next layer height to be used. However, a substantialamount of empirical and statistical modeling for identifying the curedlayer shape and its relation to the surface roughness parameter Ra for agiven additive manufacturing technique needs to be performed.

In order to overcome these limitations and to accomplish the ultimateobjective of adaptively slicing a generic BRep model with a reasonablesimplicity, the volume deviation-based adaptive slicing technique hasbeen developed and implemented.

In the volume deviation-based approach developed in this thesis, theentire volume of the cusp is calculated in order to use as a measure forestimating the geometric deviation of the layered part. The concept ofcusp volume is illustrated in FIG. 56, where the geometric deviationbetween a hemispherical part and the corresponding additive manufacturedpart is highlighted. FIG. 56 illustrates a cusp volume for ahemispherical part. As is clear from the illustration, the geometricdeviation of each 2.5D layer with the corresponding 3D layer of the partis labeled as the cusp volume.

In order to adaptively slice the part, at each slice height, the cuspvolume is computed and used as a measure to determine the height of thenext layer. However, the cusp volume may dramatically change over theheight of a part as it is a function of the perimeter of thecross-section, layer thickness and the angle made by the local surfacetangent vector with the build direction. Hence, it is not possible touse a constant cusp volume criterion for determining the layerthickness. In order to alleviate this difficulty, the cusp volume isnormalized by the volume of the 3D slice of the part to give an estimateof the percentage volumetric error within each layer of the additivemanufactured part as compared to the original geometry as shown inEquation 24.

${{\% \mspace{14mu} {VolumetricError}} = \frac{{Cusp}\mspace{14mu} {Volume}}{3\; D\mspace{14mu} {Slice}\mspace{14mu} {Volume}}},$

An upper bound on the % VolumetricError is placed and the layerthickness at each slice height is determined so as to satisfy this upperbound criterion. At each slice height along the length of the part, the% VolumetricError is first estimated using the maximum possible layerthickness. If the computed error is less than the maximum bound, themaximum layer thickness is used. If not, the layer thickness issuccessively converged to a value that yields the specified maximumerror using a ‘bisection’ scheme. If the resulting layer thickness isgreater than the minimum layer thickness that may be built, then it isused as next layer height. Otherwise, the next layer height is set tothe minimum layer thickness and the operation is repeated.Implementation details of this approach using ACIS kernel are givennext.

The pseudo code for the adaptive slicing operation using volumedeviation approach is shown in Algorithm 12. The part of the given nameis first loaded into the program and all the important ACIS parameterslike resolution are set. The bounding box of the part is computed nextto identity its min and max extents. Slicing is started at a height justslightly above minZ. For each slice height minZ<z<maxZ, the slicecontour is computed and slice image created.

Algorithm 12 Adaptive Slicing Algorithm. 1: load the given part andstore in wig 2: compute bounding box and store the bounds in min and max3: for z:= minZ to maxZ do 4:  create horizontal plane at height z5:  compute slice by intersecting the plane with the part 6:  createimage from slice 7:  z = z + layerThickness(wig, z) 8: end for

Once the slice image is created, the slice height of the next layer isdetermined by passing the part (wig) and the current slice height (z) toa function called layerThickness. The pseudo-code for this function isshown in Algorithm 13.

Algorithm 13 computing layer thickness 1: function layerThickness(wig,z) 2: low ← z 3: high ← z + MAXTHICKNESS 4: deviation =computeDeviation(wig, z, MAXTHICKNESS) 5: thickness = MAXTHICKNESS6: mid = 0 7: while deviation ≠ 0 and |deviation − MAXTHICKNESS| > TOLdo   8: ${mid} = \frac{{high} + {low}}{2}$ 29:  thickness = mid - z10:  if thickness > MINTHICKNESS then 11:   deviation =computeDeviation(wig; z; thickness) 12:   if deviation = 0 then13:    break 14:   else 15:    if deviation > MAXDEVIATION then16:     high = mid 17:    else 18:     low = mid 19:    end if 20:   endif 21:  else 22:   thickness = MINTHICKNESS 23:   break 24:  end if25: end while 26: end function

In this algorithm, three height trackers denoted by low, mid and highare used. For finding the layer thickness at height z, these threetrackers are first set to z, 0 and MAXTHICKNESS (denotes the maximumlayer thickness that may be built) respectively. First the % volumedeviation of the part at height z is computed at the maximum allowablelayer thickness. If this deviation is either non zero or greater thanthe maximum allowable volume deviation denoted by MAXDEVIATION, theheight of the next layer is adjusted using a scheme similar to thebisection method in root finding (until the volume deviation is in thevicinity of the maximum allowable volume deviation).

So, if at MAXLAYERTHICKNESS, the volume deviation is greater than theMAXDEVIATION, the height marker mid is adjusted to its new value asshown in Equation 25:

$\begin{matrix}{{{mid} = \frac{{high} + {low}}{2}},} & {{Equation}\mspace{14mu} {(25).}}\end{matrix}$

The volume deviation at this new height given by mid is then computed.If it is still higher than MAXDEVIATION, then high is set to currentvalue of mid so that in the next iteration, the volume deviation iscomputed at a lower height. If the volume deviation at the current valueof mid is lower than the MAXDEVIATION, then low is set to the currentvalue of mid so that in the next iteration, the volume deviation iscomputed at a higher z height. In this manner, through successiveiterations, the value of mid converges to a z height where the volumedeviation is within a tolerance range denoted by TOL in the vicinity ofMAXDEVIATION. Once the value of mid has converged to a stable value, thenext layer height is computed as shown in Equation 26 and returned back.

thickness=mid−z,  Equation (26).

This ensures that at each slice height z the part is sliced at themaximum possible layer thickness to satisfy the volume deviationcriteria in order to obtain the minimum number of slices for the partthereby reducing the total build time while also maintaining accuracy.The implementation of the function computeDeviation which is used forcalculating the volume deviation of a given generic BRep part wig at aslice height z and a layer thickness (denoted by thickness) is fairlysimple and easily scalable to parts of arbitrary complexity. The pseudocode of this function showing the various operations that need to becarried out for computing volume deviation is shown in Algorithm 14.

Algorithm 14: Computing % Volume Deviation. 1: functioncomputeDeviation(wig, z, thickness) 2: //compute 3D slice: 3: block ← acuboid of height equal to thickness 4: 3DSlice ← solid geometry obtainedfrom intersection of wig and block 5: //compute 2.5D slice: 6: slicePlane ← a plane created at height z + thickness 7: contour ← intersectionof wig and sliceP lane 8: 2:5DSlice ← sweep contour down by a distanceequal to thickness 9: //compute volume lost: 10: cuspVolumel ← subtract2:5DSlice from 3DSlice 11: //compute volume gained: 12: cuspVolume2 ←subtract 3DSlice from 2:5DSlice 13: //compute volume of 3D slice:14: 3DVolume ← volume of 3DSlice 15: //compute % volume deviation:   16:$\left. {deviation}\leftarrow{\frac{{{cuspVolume}\; 1} + {{cusp}\; {Volume}\; 2}}{3{DVolume}}*100} \right.$17: return deviation back to the calling function 18: end function

First, the 3D slice geometry is computed. In order to do this, arectangular cuboid of height equal to the given layer thickness (denotedby thickness) is created and stored in the variable named block. The 3Dslice geometry may then be computed by performing a solid intersectionoperation in ACIS between the given part wig and the cuboid denoted byblock. Next, the 2.5D slice (the geometry of each printed layer assumingrectangular walls) geometry is computed by the following steps

a) creating a slice plane at height z+thickness,

b) computing the intersection of the plane with the given CAD part wigto get the 2D slice contour,

c) sweeping the 2D slice contour vertically down by a distance equal tothe current layer thickness.

Once, the 3D and 2.5D slices are computed, the volume lost by thelayered part (denoted by cuspVolume1) at the given height z and thegiven layer thickness is determined by performing a subtractionoperation in ACIS using the 3D slice as the ‘blank’ body and 2.5D sliceas the ‘tool’ body and computing the volume of the resulting geometry.Similarly, the volume gained by the layered part (denoted bycuspVolume2) is determined by swapping the blank and tool bodies fromthe previous step and computing the volume of the resulting geometry.Finally, the % volume deviation may be computed as shown in theexpression on Line 16 in Algorithm 14, where 3DVolume denotes the volumeof the 3D slice. FIGS. 57a-57f illustrate each of these steps forcalculating the volume deviation while slicing a sample CAD part inaccordance with various aspects as described herein.

The effect of adaptive slicing on a sample CAD part composed of threedifferent primitives (cylinder, cone and a sphere) and a free formcross-section is shown in FIG. 58. FIG. 58 is a sample CAD partadaptively sliced using the volume deviation approach. The minimum andmaximum layer thicknesses used were 0.001 inch and 0.1 inchesrespectively. A maximum volumetric deviation of 2% is used as theadaptive slicing criteria. The following observations may be made fromFIG. 48:

(a) The maximum layer thickness of 0.1 inch is used for the region withvertical cylindrical cross-section since the volume deviation for thisregion is zero.

(b) A more or less constant layer thickness which is smaller than themaximum value is used for slicing the conical section. The slightvariation in the layer thickness in this region is caused due to thefact that % volume deviation is a relative measure and it changes withrespect to the cross-section location along the height of the part.

(c) For the spherical section, the layer thickness is varied graduallywith thickness decreasing towards the top.

(d) For the free form section, the layer thickness is variedcontinuously, with thickness increasing or decreasing depending on thelocal surface complexity.

FIG. 59 provides a chart 5900 of variation of layer thickness vs. heightz for sample part. FIG. 59 provides a plot of how the layer thicknessvaries along the height of the part to give a more clear illustration ofthe observations presented above. It may seen that the layer thicknessranges between the maximum and minimum thickness specified in thealgorithm.

FIG. 60 provides a chart 6000 of the percentage volume deviation vs.height for sample part. FIG. 60 gives a plot of % volume deviationpresent in each layer along the height of the part and how this variesfor the adaptively slicing as compared to uniform slicing at the maximumlayer thickness. As may be clearly seen, the adaptively sliced part hasa volumetric deviation of at most 2% as specified by the maximum boundin the algorithm whereas, for the uniformly sliced part, the volumetricdeviation fluctuates through a wide range from 0% to nearly 35% as afunction of location in the build direction. FIG. 61 provides a chart6100 of percentage total volumetric error vs. height for sample part.FIG. 61 gives a plot showing the variation of the total absolute volumein (in3) lost or gained in the part for both the adaptive slicing anduniform slicing.

From the results shown, it is evident that this approach of using %volumetric deviation as a criterion for adaptive slicing works verywell. Since it computes the full three dimensional volume of the cusp,this approach is free of the limitations of the area deviation approachfor slicing BRep models.

It is to be noted that the % volumetric deviation metric is a relativemeasure as compared to the cusp height metric (which is an absoluteone). However, as shown by the results, this approach yieldssatisfactory outcomes and its evident simplicity (quicker computationtime as a consequence) and scalability to handle generic BRep modelswith more complex geometry (as compared to only parametric surfacesplines handled by Kulkarni and Dutta) give it the advantage. Therelativeness of the volume deviation metric may be alleviated by havingmore designer knowledge of the parts being built (like the minimumfeature sizes, maximum curvature regions etc.) while setting theparameters (minimum and maximum layer thickness ranges and the maximumvolume deviation bound) in the slicing algorithm.

As future scope of this work, for the specific HP turbine blade designsintended for fabrication via LAMP, empirical studies may be performed torelate the % volumetric deviation to the absolute surface roughnessparameter Ra of the fabricated parts in order to infer a more accurateparameter range for the slicing algorithm. However, for successfullyfabricating adaptively sliced parts, some hardware changes need to bemade in the LAMP machine as well. In its current configuration, it isnot possible to change the exposure time dynamically in a build in anautomated fashion (It may still be specified manually before theexposing each layer but becomes very tedious for large builds). Thiscapability needs to be achieved in order to cure layers of arbitrarythickness. Controlling the wet layer thickness while re-coating eachfresh layer is also crucial as it is dependent on phenomena like surfacetension, suspension rheology etc. Once these changes are implemented, itis expected that a simple and scalable adaptive slicing algorithm likethe one presented here would greatly improve the part quality.

The other major approach pursued herein to address the issue of stairstepping is through gray scaling and dithering. The basic idea behindusing gray-scaling and dithering in LAMP is to effectively modulate thecure depth in a single exposure by using screened gray scale regions inthe build images in place of using the original all white regions forthe cured regions in the slice images. The stair stepping effectobserved in additively manufactured parts, as discussed previously, is aresult of the fact that the cured layers have 2.5D geometry with aconstant depth across the entire region of exposure. For surfaces thatare facing downward (i.e surfaces whose normal vectors make an anglegreater than 90° and less than 270° with respect to build direction),this means that the cured layer overshoots the part geometry at theedges. This effect is illustrated in FIGS. 62a and 62b . FIGS. 62a and62b illustrate stair stepping caused on downward facing surfaces whileusing all white build images.

For a 3D CAD model shown in FIG. 62a referenced at 6200 a, if all-whiteslice images are used to represent the exposure dose for curing eachlayer of a part, the resulting cured layers overshoot the actual surfaceprofile as shown in FIG. 62b referenced at 6200 b.

In order to rectify this overshooting effect, the exposure dose that thematerial system receives needs to be modulated locally at the edges ofeach exposure image (where the full cure depth leads to overshoot) toget a cured profile that represents the surface profile more accurately.Energy dose (E) is a product of the light intensity (denoted by I andhas units of W/m²) and exposure time (t) as shown below:

E=I*t,  Equation (27).

Thus, one method of locally modulating the exposure energy dose Einvolves manipulating exposure time t. However, in the current LAMPequipment, there is no facility to locally manipulate the exposure timeswithin each exposure. An alternate method for manipulating the exposuredose involves by manipulating the light intensity. Since LAMP and mostother projection systems use a single light source with a fixed poweroutput, locally manipulating the light intensity would is also verychallenging. As an alternative to local manipulating the actual lightintensity, gray-scaling followed by dithering is used to manipulate theeffective light intensity incident upon the material.

Details of the algorithm and the methodology followed for generatinggray scale images in order to modulate the cure depth within eachexposure to reduce the stairstepping effect on downward facing surfaces,are presented in this section. The cure depth C_(d) is a function oflight intensity I, resin parameters sensitivity D_(p) and criticalenergy E_(c) and exposure time t. As previously discussed, the exposuretime t is held constant in this approach. Through the experimentalinvestigations presented in the previous sections, it was determinedthat rest of the parameters are in turn functions of the gray scalevalue G. This functional dependence on gray scale value G is shown inEquation 39.

$\begin{matrix}{{C_{d} = {{D_{P}(G)}\ln \frac{{I(G)}t}{E_{c}(G)}}},} & {{Equation}\mspace{14mu} {(39).}}\end{matrix}$

These functional dependencies have been explicitly identified in theprevious sections. Therefore, the final expanded form of the expressionrelating C_(d) and gray scale value G for HDS superfine screeningresolution may be written as follows:

$\begin{matrix}{{C_{d} = {\left( {{22.1G} + 193.1} \right)\ln \frac{{GI}_{o}t}{{35.6G} + 101.8}}},} & {{Equation}\mspace{14mu} {(40).}}\end{matrix}$

where Io is the full light source intensity from an all white exposurewhich was measured to be 1.6 mW/cm² for the light source used in LAMP.Therefore, using the expression in Equation 40, for a given exposuretime t, the gray scale value G that results in the required cure depthCd may be computed. The details of the algorithm to identify therequired cure depth Cd and thereby the required gray scale value G ateach pixel in the slice image are given next.

The direct slicing algorithm may be extended to output gray scale sliceimages instead of the usual black and white images. The pseudo code foraccomplishing this is presented in this Algorithm 15.

Algorithm 15: Gray Scale slice image generation. 1: wig ← given part 2:for each slice height z along the height of the part do 3:  //compute 3DSlice: 4:  block ← a cuboid of height equal to layerThickness5:  3DSlice solid geometry obtained from intersection of wig and block6:  //compute 2D Slice: 7:  slicePlane ← plane at a height of z +layerThickness 8:  2DSlice ← contour obtained from intersection of wigand slicePlane 9:  //compute Slice Image Pixel Values: 10:  for eachpixel in the slice image corresponding to the 2D slice do 11:    (x, y)← coordinates corresponding to the pixel 12:    C_(d) ← thickness of3DSlice at (x, y) 13:    t ← exposure time corresponding to a cure depthequal to layerThickness 14:    G ← gray scale value solved from Equation40 using C_(d) and t 15:    pixelValue ← G * 255 16:  end for 17: endfor

The given CAD model is first loaded into the program and assigned to thevariable wig. For each slice height z along the height of the part,first a three dimensional slice, denoted by 3DSlice, is computed inorder to identify the accurate geometry that needs to be cured. This isaccomplished by creating a cuboid, denoted by block of thickness equalto the build layer thickness denoted by layerThickness and computing theintersection of it with the given part denoted by wig. Next, the 2Dslice contour denoted by 2DSlice is computed at a heightz+layerThickness by creating a slice plane at this height and computingits intersection with wig. Now, for each pixel in the slice imagecorresponding to the slice height z+layerThickness, first thecorresponding coordinate values denoted by (x; y) of the pixel areidentified. The required cure depth Cd that needs to be achieved isdetermined by computing the thickness of the 3D slice geometry at thesecoordinates. The exposure time t is fixed and corresponds to a curedepth equal to the full layer thickness used in the build. Using thesevalues for Cd and t in Equation 40, the gray scale factor G may besolved for by using any of the standard root finding techniques likeNewton-Raphson or Bisection method. Once the required gray scale value Gat the current location is determined, the corresponding pixel value ofthe slice image is set to G _255 (For an 8-bit gray scale image, likethe one being created in this case, a value of 255 corresponds to fullwhite and a value of 0 corresponds to full black). In this manner, thegray scale values for each of the pixels in the slice image aredetermined and the slice image is created.

FIGS. 63a-63d illustrate a method 6300 for producing a gray scale imagein accordance with various aspects described herein. FIG. 63a referencedat 6300 a shows the sample part used for computing gray scale sliceimages. FIG. 63b referenced at 6300 b shows the process of identifyingthe required cure depth corresponding to each pixel of the slice image.From the cured depth determined by this process of ray intersectionswith the 3D slice, the gray scale value required at each pixel value mayin turn be computed from the cure depth model established in Equation40. The gray scale slice image obtained from this process is shown inFIG. 63c referenced at 6300 c. FIG. 63d referenced at 6300 d shows azoomed in view of the dithered gray scale region obtained by ditheringthe gray scale slice image.

For the sample part shown in FIG. 63a referenced at 6300 a, one samplelayer is cured for demonstration of the concept. FIGS. 64a and 64billustrate gray scale exposure results. FIG. 64a referenced at 6400 ashows the cured profile obtained with an all white exposure. Asexpected, the profile is more or less 2.5 D cross-sectional. The curedprofile of the same layer now exposed with the gray scale slice imageobtained using the process discussed in the previous section is shown inFIG. 64a referenced at 6400 a. As may be seen, the cured profileobtained with the gray scale exposure is very close to the actual 3Dslice geometry of each layer for the sample part shown in FIG. 64areferenced at 6400 a.

These single layer cured profiles serve as a proof of concept.Multilayer parts may easily be built using this exposure technique toyield smooth downward facing surfaces. Moreover, since the cure profilemay now be accurately controlled, higher layer thicknesses may be usedin builds without any compromise on part accuracy and surface smoothnessthereby potentially reducing build times as well.

As discussed in the previous section, the cure width Cw obtained is aresult of the complex interaction of several parameters which is verydifficult to model accurately. Hence, in order to understand the curedepth behavior of LAMP suspensions, a simple experimental study isproposed. From experience, four important parameters are singled out forstudying their specific effects on cure width Cw. They are:

(a) Feature size,

(b) Peak light intensity,

(c) UV absorber concentration, and

(d) Photoinitiator (PI) concentration.

Discrete values for each of the parameters were identified and the curewidth characteristics at each of these parameters are determinedexperimentally. Cure widths were determined by exposing squares of knownlength over a glass slide and by measuring the deviation of the curedsquare lengths obtained. FIG. 65 illustrates a sample exposure imagewith a known constant square length with ten different tiles. FIG. 66illustrates cured squares obtained by exposing the image in FIG. 65.FIG. 65 shows a sample image with known squares that is used forexposure and FIG. 66 shows an image of the corresponding cured layersobtained.

It is to be noted that each tile in the exposure image in FIG. 65 isexposed at a different exposure dose and hence the resulting squarelengths obtained in the cured square tiles shown in FIG. 66 aredifferent. The corresponding cure widths C_(w) at each of the exposuredoses is computed as follows:

$\begin{matrix}{{C_{w} = \frac{I_{cured} - I_{o}}{2}},} & {{Equation}\mspace{14mu} {(60).}}\end{matrix}$

where lcured is the square length obtained after curing each tile, andlo is the nominal square length in the exposure Image. In this manner,at discrete values of each of the parameters (a), (b), (c), and (d), thecure width trends with respect to the energy dose are identified.Critical energy dose and sensitivities for cure width Cw analogous to Ecand Dp for the case of cure depth Cd are introduced. For the sake ofclarity, from here on, a different notation is used for identifying thecritical energy doses and sensitivities corresponding to cure depth andcure width respectively. The critical energy dose corresponding to curedepth Cd is denoted from here on by Ed c and the sensitivity for curedepth is denoted by Dd p. Similarly, the critical energy dose andsensitivity for cure width Cw are represented by Ew c and Dw prespectively. The extra superscripts ‘d’ and ‘w’ are added to the usualparameters Ec and Dp where ‘d’ denotes depth and ‘w’ denotes width.

A new parameter known as broadening depth Bd is introduced, which givesthe maximum cure depth that may be achieved before the layers begin tocure in the width direction. It is determined by computing the curedepth obtained at an energy dose equal to the cure width critical energydose Ew c at which lateral curing just begins to occur as shown inEquation 61.

$\begin{matrix}{{B_{d} = {D_{P}^{d}\ln \frac{E_{c}^{w}}{E_{c}^{d}}}},} & {{Equation}\mspace{14mu} {(61).}}\end{matrix}$

This is a good measure for characterizing the side-scatter induced curewidth broadening of each composition. Ideally, the composition should beoptimized for maximum broadening depth in order to get deep cured partswith good layer-to-layer bonding and minimal excess side scattering.

The parameters introduced here to analyze the cure width characteristicsof the material system for LAMP are analogous to ones for characterizingthe line widths of the LAMP suspension. However, it will be shown thatthe results obtained here deviate from the ‘quasi-Beer-Lambert’ lawintroduced in her thesis. These differences may be attributed tofollowing:

1) differences in the exposure set up used,

2) difference in the curing times used,

3) difference in the method by which cure widths Cw are calculated.

The results obtained from the experimental investigations using themethodology described in this section are given next.

Three scenarios may present the need for support structures in typicaladditive manufacturing processes. These are re-listed here for the sakeof clarity:

(a) Surfaces with large overhang.

(b) Surfaces or geometries that result in floating Islands.

(c) Geometries with the potential to topple over.

As previously mentioned, the degree to which each of these scenariosnecessitate supports changes with each additive manufacturing process.For example, selective laser sintering (SLS) does not need any specialsupports for either of the scenarios since there is always a bed ofunsintered powder acting as support. Fused deposition modeling (FDM) onthe other hand, requires supports for all of these scenarios sincematerial is only deposited in the region enclosed by the part geometryand the rest of the build volume is empty unlike in the case of SLS. Forthe stereolithography (SLA) process, the need for supports liessomewhere in between the spectrum of these two extremes. Since the buildvolume in SLA consists of a viscous resin, in some instances (based onthe part geometry), the buoyancy force offered by the viscous mediumsufices to support the parts from toppling over, thereby eliminating theneed for supports in this scenario.

From the previous discussion it is clear that, although some commonscenarios that necessitate support structures exist, the degree to whichthey impose the need for supports varies with respect to the additivemanufacturing process in consideration. The need for supports withrespect to each of these scenarios specific to the LAMP process isdiscussed in this section. The LAMP process, as previously discussed,aims to build ceramic molds for the casting of high-pressure turbineblades. Hence the need for supports in the LAMP process specific to theneeds of the geometries that arise in HP turbine blade molds isconsidered. FIG. 110 illustrates the features found in a representativeHP turbine blade mold.

All the geometric features observed in the figure are intended for thecooling of internal and external surfaces of the blade. Some prominentfeatures like the leading edge, trailing edge, film cooling pins (coolthe leading edge and mid chord portion of the external surface of theblade), mid-chord serpentine (creates a serpentine passage for internalair flow in the mid chord region), leading edge cavity (supplies coolingair to the leading edge film cooling pins), tip cap (creates an aircavity for cooling the top edge of the blade), pin fins (cool the narrowcross-section of the trailing edge) are annotated. While building such acomplex geometry, each of the three scenarios demanding supportstructures are encountered and the means by which they may be handled inLAMP is presented next.

While building the complex geometry of the HP turbine blade molds,several overhangs do occur. FIG. 67 shows the native orientation of theblade mold. When built in this orientation, features that define the tipcap of the blade cause very large overhangs leading to a failure of thebuild. However, from previous experience, for the typical HP bladegeometries, an orientation may be found which minimizes these overhangsthereby resulting in successful builds. Such an orientation is shown inFIG. 68, which enables the tip cap features which were previouslycausing build failure to grow more gradually from their root at thetrailing edge. FIG. 68 illustrates a build orientation that reducesoverhangs observed in the original orientation.

Thus, for the kind of geometries encountered in the LAMP process, theproblem of adding supports to overhanging structures is not so crucialand a build orientation may be found that will result in tolerableoverhangs that will lead to successful part builds. This is idealbecause any additional support structure added would be totally internalto the built part and impossible to remove. This leads to additionalunintended features in the cast blades which will alter the coolingcharacteristics of the intended design. However, if in the future, ablade geometry is encountered which does not have any viable orientationthat yields tolerable overhangs, then this support scenario needs to beaddressed.

The issue of floating islands while building complex geometries liketurbine molds using the LAMP process is a significant one. In mostsimple geometries, an orientation may be found which does not result inany floating islands. However, for the parts with the kind of complexityshown in FIG. 67, it is not typically possible to find any occurrencethat will eliminate the formation of floating islands. Even in theorientation that was shown in FIG. 69, which minimizes overhangingstructures, floating islands form when the bases of the mid-chordserpentine and the leading edge cavity begin to form. FIG. 69illustrates a build orientation that reduces overhangs observed in theoriginal orientation. FIG. 70 illustrates a cross-section of the part asthe base of the leading edge cavity is being built. The featurehighlighted by the box clearly does not have any previously builtfeature supporting it.

When such unsupported features are cured, since there is no featurebeneath it to adhere to, the shrinkage stresses have a greater effect onthe feature and it curls up. Also, the re-coating process impartssignificant shear stresses on the layers as it sweeps through the buildarea. As the blade sweeps over with a layer of viscous ceramic loadedsuspension underneath it, a boundary layer is formed which imparts dragforces on the platform. The suspension was observed to be non-Newtonianbut ignoring this fact, a rough estimate of the shear forces may bemade. The viscosity of the slurry in the velocity ranges of there-coating process was measured to be in the 400-450 centi poise range.The re-coating blade travels a distance of 26 cm in 6 seconds and is atheight of 200 _m above the build platform. At this speed and viscosity,assuming Newtonian behavior and a linear velocity profile, the shearstresses imparted on the part will be of the order of _100 Pa. Due tosuch high shear forces and the curling up effect of unsupported featuresdue to shrinkage stresses, any unsupported features formed will be sweptaway by the re-coating arm causing the build to fail.

Hence support structures are necessary for any geometries that producefloating islands during a build, in order to obtain successful parts.However, as discussed previously, all of the geometric features,supports or otherwise are enclosed within the outer shell of anintegrally-cored mold and removing these supports post-build isimpossible. This results in additional unintended features in the castblades which might adversely impact the designed cooling performance ofthe molds. This issue of floating islands is probably the onlylimitation potentially preventing the LAMP process from building bladedesigns of any arbitrary complexity.

However, it must be noted that the current blades are designed formanufacture through conventional investment casting process capabilitiesand constraints. As the LAMP process enters into full production and thecastability of the parts produced through the process is successfullydemonstrated, there is immense scope for advanced mold design specificto this technology. The work presented in this thesis is a first steptowards this goal of design for manufacturing specific to the needs ofthe LAMP process.

The final scenario that requires supports is the case of part topplingover due to its own weight as the part is being built. In the case ofthe LAMP process, requirements of supports of this kind is quite weak.The parts are attached to the build platform quite rigidly with the helpof a mesh structure. The parts are built with a conformal scaffoldsurrounding them. Therefore, as the parts are built, there isscaffolding all around in the build volume thus eliminating thepossibility of the parts toppling over due to gravitational moments.

Thus, in retrospect, of all the scenarios requiring support structures,only the scenario resulting in floating islands poses a serious threatfor part failures in the case of LAMP process and therefore needs to beaddressed further. Details on the methodology followed foralgorithmically identifying the geometries that result in floatingislands from input CAD models and the methodology for creating supportstructures are given next.

In order to optimally position support structures, first there needs tobe a method of algorithmically identifying the geometries which resultin these floating islands during a part build. The details of such analgorithm developed for the purpose of identifying floating islands fora part being built in a given direction is given in this section. ACISkernel was again used for implementing the algorithm and hence it worksdirectly on CAD models. The pseudo code for this procedure is shown inAlgorithm 16.

Algorithm 16 Identifying Floating Islands.   1: wig ← the given CAD part  2: layerThickness ← layer thickness used in the build   3: (X_(min),Y_(min), Z_(min)) ← compute minimum extents of the part   4: (X_(max),Y_(max), Z_(max)) ← compute maximum extents of the part   5: for each Zlocation along the height of the part do   6:  //compute slice at heightZ   7:  (X_(bmin), Y_(bmin), Z_(bmin))₁ ← (X_(min), Y_(min), Z −layerThickness)   8:  (X_(bmax), Y_(bmax), Z_(bmax))₁ ← (X_(max),Y_(max), Z)   9:  block1 ← a cuboid created with extents specified by(Xbmin; Ybmin;Zbmin)1 & (Xbmax; Ybmax;Zbmax)1   10:  3DSlice1 ← geometryobtained form the intersection of wig and block1   11:  //compute sliceat height Z + layerThickness   12:  (X_(bmin), Y_(bmin), Z_(bmin))₂ ←(X_(min), Y_(min), Z)   13:  (X_(bmax), Y_(bmax), Z_(bmax))₂ (X_(max),Y_(max), Z + layerThickness)   14:  block₂ a cuboid created with extentsspecified by (X_(bmin), Y_(bmin), Z_(bmin))₂ & (X_(bmax), Y_(bmax),Z_(bmax))₂   15:  3DSlice₂ ← geometry obtained from the intersection ofwig and block1   16:  //check for floating islands in 3DSlice₂  17:  for each disconnected lump i in 3DSlice₂ do   18:    for eachdisconnected lump j in 3Dslice₁ do   19:      check for intersectionbetween lumps i & j   20:    end for   21:    if no intersections foundthen   22:      lump i in 3DSlice₂ is a floating island   23:    end if  24:  end for   25: end for

The given part is first loaded into the algorithm and its minimum andmaximum extents are computed. At each Z location along the height of thepart, a cuboid denoted by block1 with a cross-sectional area equal tothe cross-sectional area of the bounding box of the part and a thicknessequal to layer thickness is created. A solid body intersection iscomputed between the part denoted by wig and block1 to yield a threedimensional slice denoted by 3DSlice1 at height Z of the part.Similarly, a three dimensional slice denoted by 3DSlice2 at heightZ+layerThickness is computed. At the height corresponding to thefloating island illustrated in FIG. 70, the two slices computed usingthe previous steps are illustrated in FIGS. 71a and 71b . FIGS. 71a and71b illustrate 3D slices of successive layers at the locationcorresponding to the floating island shown in FIG. 70. For illustrativepurposes, slices separated by a few layers are shown and hence theapparent large overhangs. For successive slices, the overhang will bevery small but so is the floating feature generated and hence it will bedifficult to perceive.

Although, in the Figure, the slices look two dimensional because of verythin layer thickness (100 _m), they are in fact three dimensionalbecause of the way they were created. Each of the disconnected solidregions in these slices are stored as a lump in the ACIS data structure.In order to determine if there are any floating islands in the secondslice, each of the lumps of this slice is checked for intersection witheach of the lumps of the first slice. If there exists a lump in thesecond slice, which does not intersect with any of the lumps in thefirst slice, it is classified as a floating island and supportstructures need to be created. By repeating this sequence of operationsfor every successive pair of slices along the length of the part, allthe features that lead to floating islands during a part build may beidentified. This operation may be repeated for different orientations ofthe part, and the orientation that yields the minimum number of floatingislands may be selected. The details of the algorithm to generatesupports for the floating islands identified using this approach ispresented next.

In most of the previous work presented, supports were generated onlyalong the build direction which either extend all the way down to thebase of build platform or until the next immediate geometric feature.This approach does not work for LAMP as all of the supports will becompletely encapsulated by the shell and thus cannot be removed. Hence,creating long slender supports all the way to the base will completelydisrupt the intended cooling designs. Instead, the approach presentedhere, tries to connect the identified floating island to the immediatesurrounding geometry with minimal support length to have minimal impacton the intended design. Note that, the geometries that these supportstructures connect to need not be directly underneath the floatingisland along the build direction unlike the previous approachespresented. The pseudo code for such an approach is shown in Algorithm17.

Algorithm 17 Support Structure Generation. 1: origin ← centroid of thefloating island that needs to be supported 2: maxTiltAngle ← maximumtilt angle with which a support may be built 3: maxCurvature ← maximumcurvature allowed at the point of contact 4: n ← the number oforientations user wants to output 5: r ← nominal radius of the support6: candidateOrientationList ← discrete orientations within the ”cone”underneath origin 7: for each orientation i in candidateOrientationsList do 8:  shoot a ray from origin to the surroundinggeometry of the part 9:  check for smoothness of the surface at thepoint of intersection with the ray 10:  curvature ← local surfacecurvature at intersection point 11:  if surface is smooth and curvature< maxCurvature then 12:    support: direction ← orientation i13:    support:length ← length of the ray in this direction 14:    list← support 15:  end if 16: end for 17: sort the identified supportorientations in list w.r.t length in ascending order 18: for i:= 1 to ndo 19:  retrieve i^(th) orientation from the sorted orientations in list20:  sweep a circle of radius r from origin along the ray in orientationi 21:  output the part 22: end for

The algorithm takes in four parameters as input as follows:

(1) The centroid of the floating island at which supports need to begenerated denoted by origin.

(2) The maximum tilt at which supports may be built denoted bymaxTiltAngle.

(3) The number of potential orientations that the user wants to outputdenoted by n.

(4) The nominal radius of the supports as specified by the user denotedby r.

First, a list of possible candidate orientations along which a supportmay be built is created by discretizing the “cone” underneath originwith a vertex angle equal to maxTiltAngle. For each of these candidateorientations, rays originating from origin are generated and theirintersections with the part geometry is computed. At each of thesepoints of intersection, the smoothness of the surface is measured. Iflocal surface curvature is high, there is a good possibility that itcorresponds to a cooling feature and this orientation is abandoned.Likewise, if the intersection point is near to the boundary of two ormore surfaces and the adjoining surfaces do not maintain continuity,this orientation is abandoned as well as it was observed from experiencethat shrinkage stresses accumulate at such corners and cause thesupports or other slender structures to fail. After eliminatingorientations that connect to non smooth surfaces in this manner, therest of orientations are stored as potential directions for supportpropagation. The lengths of the rays originating from origin in each ofthese potential directions are computed and the list of potentialorientations is then sorted in the ascending order w.r.t their lengths.For the first n orientations in the sorted list, cylindrical supportswith radius r are created by sweeping a circular cross-section along theray until it connects to the part.

FIG. 72 illustrates various supports generated on the sample HP bladeshown in FIG. 67 using this method. As may be seen, of the variouscandidate orientations, many of the orientations are discarded becausethey either intersect the surface at regions of high curvature or arevery long. The support structure highlighted in green is the one that ispreferred as it is the shortest and also interesects the part at a lowcurvature region.

In many of the instances experienced in parts of the form shown in FIG.67, the features that lead to floating islands grow continuously (i.e,grow from a small area floating region to a larger feature) and hencefrom past experience it is known that only one support of the typehighlighted in green in FIG. 72 is enough. FIG. 72 illustrates supportsgenerated by the algorithm. However, when the features abruptly resultin large floating islands, this algorithm may easily be extended forproducing multiple supports. For supporting large floating features, anadditional parameter that indicates the maximum amount of overhang aparticular support feature of a given size may support needs to beincorporated in to the algorithm. Based on this parameter, the area ofthe large floating island may be sub divided into smaller regions andthe procedure may be applied for each of the smaller regions with anadditional constraint to produce non intersecting supports.

As was previously noted, any support structures incorporated into themold to yield successful LAMP builds are completely encapsulated withina conformal shell. Hence there is no way to remove these structures fromthe mold post build and this will in turn result in additionalunintended features in the cast blades. Although this is a limitation ofthe LAMP process, it must be noted that the current blades were designedwith the conventional manufacturing techniques in view and hence thereis immense scope for design for manufacturing specific to the needs ofthe LAMP process. In order to demonstrate this, the performance analysisof the design resulted by the incorporation of a sample supportstructure like the one highlighted in FIG. 72 is given in this section.Intuitively, the addition of a support feature like that will reroutesome of the cooling air from the mid chord serpentine channel to theleading edge cavity. In doing so, it might not only deprive some of theupper impingement cooling holes but also stymie the lower mostimpingement jets at the leading edge. Also, because of the cooling airrerouting, there might not be enough mass flow left in the mid chordserpentine to cool all the other features like the tip cap etc. itsupplies cooling air to. Hence in order to investigate this, the flowand thermal analysis of this support feature was performed. The detailsof these simulations and the results obtained will be discussed below.

In order to simply the meshing process and reduce computational times,the geometry was simplified to a representative but more amenable one. Aconstant representative heat flux boundary condition of 25 MW/m² wasapplied to the leading edge wall. A constant velocity of 20 m/s wasapplied as the input flow condition at the base of the serpentinechannel with a turbulence intensity of 5%. The simulation was carriedout to solve the reynolds averaged navier stokes equations and thethermal equation for the each of the cases corresponding to the nativeand modified (with support added) geometry. FIGS. 73a and 73b illustratea temperature profile obtained on the internal wall of a leading edgewith and without a support structure. It may be clearly seen that,unlike what was expected, the temperature profile in the case of thesupport added is much lower than the case without a support. There is ahot spot at the lower region of the leading edge for the case without asupport and the addition of a support reduces the peak temperatureoccurring on the leading edge wall significantly. FIGS. 74a and 73billustrate velocity streamlines in an internal cavities. It may be seenthat in the case without the support, the flow streams from the lowermost impingement jets are unable to reach bottom most region of theleading edge cavity wall which is not the case for the supportedgeometry. It may also be seen that, unlike what was intuitivelyexpected, the support structure does not stymie the flow of the lowerimpingement may be clearly seen that, unlike what was expected, thetemperature profile in the case of the support added is much lower thanthe case without a support. There is a hot spot at the lower region ofthe leading edge for the case without a support and the addition of asupport reduces the peak temperature occurring on the leading edge wallsignificantly. FIGS. 74a and 74b show the velocity streamlines of theflow to give a better understanding of temperature results obtained. Itmay be seen that in the case without the support, the flow streams fromthe lower most impingement jets are unable to reach bottom most regionof the leading edge cavity wall which is not the case for the supportedgeometry. It may also be seen that, unlike what was intuitivelyexpected, the support structure does not stymie the flow of the lowerimpingement jets and neither does it starve any of the upper impingementjets from cooling air.

Instead it increases the mass flow from the very bottom of the leadingedge cavity thereby providing better cooling overall. Also, unlike whatwas initially expected, the addition of the support structure does notsignificantly reduce the mass flow in the serpentine passage which inturn might adversely affect the cooling of other features like the tipcap. The mass flow rate difference at the exit of the serpentine channelfor the two cases was found to be very small (0.145 gm/s without supportversus 0.137 gm/s with support) and is not expected to lead to anyadverse heating of blade regions elsewhere.

Thus, in this instance it is alright to incorporate this supportfeature. Of course, in a real world situation, much further analysiswill be done to completely understand the effects of the addition of anew feature like this. The main intent for this analysis was to give abetter appreciation of the immense scope that exists for multifunctional support design (multi functional in the sense that it notonly aids in successful LAMP builds but also improves blade cooling)specific to the needs of the LAMP process.

Large Area Maskless Photopolymerization (LAMP) is a disruptive additivemanufacturing technology that has been developed for fabricating ceramicmolds for investment casting of high pressure turbine blades. The workpresented herein addressed the digital data processing and computationalneeds of the LAMP process. Several data processing algorithms likedirect slicing, STL slicing, post-processing algorithms like errorchecking, part placement and tiling etc. that enable the LAMP processwere presented. Several computational schemes to improve the partquality like adaptive slicing, gray scaling, and cure width studies forimage compensation were also discussed. Moreover, CAD datapre-processing algorithms, especially the identification of unsupportedfeatures and the generation of internal support structures suitable forthe fabrication of integrally-cored molds using LAMP process were alsopresented. Finally, some novel cooling schemes that are not currentlymanufacturable but provide improved performance over the conventionalschemes are presented. Such schemes may be fabricated using the LAMPprocess thus providing a glimpse of the potential for LAMP technology todisrupt the state-of-the-art in the investment casting of HP turbineblades. A summary of the unique contributions made in this thesis andthe scope for future research along these lines is given in thischapter.

A summary of the unique contributions made herein are listed here: (a)An error-tolerant direct slicing algorithm was presented using the ACISkernel. While previous direct slicing approaches using the ACIS kernelwere reported in literature, they all propose direct slicing as a curefor all the ills inherent in STL slicing. They claim that direct slicingwill be free of errors unlike in the case of STL slicing. It wasobserved in this thesis that this not necessarily true. Direct slicingis free of errors only when the given geometry is simple. When thegeometries are complex like the ones typically found in HP turbineblades, the CAD parts are prone to errors from two sources: 1) modelingerrors on the part of the designer and 2) due to CAD translationsrequired for direct slicing. The direct slicing algorithm presented inthis thesis is tolerant to such errors and is able to produce error-freeslices.

(b) For STL slicing, two novel approaches were presented: 1) A new wayfor reconstructing the topology information of STL meshes by extendingthe corner table data structure is presented. Using this topologyinformation, STL meshes were converted to CAD files thus aiding in errorcorrection, geometric property (volume, center of mass etc.) evaluationand modification of these meshes. 2) An extremely fast STL file slicingalgorithm was implemented. Previous STL slicing algorithms reported inthe literature use some sort of facet grouping strategy before they maybe sliced. It was shown that this only works as long as the input meshsizes are small. When the mesh sizes get very large (of the order of 5-6Million facets for turbine blade molds), these approaches takeexceedingly long (of the order of 4 days) to process and slice themeshes. The approach presented in this thesis bypasses the facetgrouping strategy completely thereby leading to several orders ofmagnitude improvement in processing time (from days to just minutes).

(c) A complete post-processing work flow including error checking, partlayout and tiling, image level geometry modification, data compressionetc. that is based on image data was presented. Most of the previouslyreported approaches work with vector data obtained from the slices.

(d) A new volume deviation based adaptive slicing approach for CAD fileswas presented. Previous approaches presented for adaptive slicing of CADfiles include determining the layer thickness based on cusp height orarea deviation approach. It was pointed out in this thesis that both ofthese approaches have their limitations. While cusp height is anabsolute criterion and a good approach for STL files, implementing thison CAD parts involves large numbers of complex calculations at eachslice location, making it difficult to scale for complex parts. Areadeviation on the other hand does not take the surface geometry intoconsideration thus seriously limiting its capability.

(e) A novel gray-scaling approach was presented to reduce the stairstepping effect on surfaces whose normal vectors point downward towardsthe base of the build. Previous gray scaling approaches reported in theliterature either have not investigated or reported the effects of grayscaling on the curing characteristics of the material. Moreover, thematerial system used in the LAMP process is loaded with a high volumepercentage of ceramic particles thereby making it radically differentfrom the material systems reported in the literature for gray scalestudies. The thesis work done by a previous member of the Direct DigitalManufacturing lab involving the characterization of the effects of grayscale on the curing characteristics was incorporated into the dataprocessing algorithms to generate gray scale images that reduce thestair stepping effects on surfaces with downward pointing normalvectors.

(f) Studies to understand the side curing behavior of the LAMPsuspension were conducted and some surprising conclusions werepresented. It was observed that the side curing was a function offeature size in the LAMP process. Any feature smaller than about 500pixels exhibits a different side curing behavior that is dependent onits size. It was also observed that the cure width varies linearly withrespect to energy dose in the LAMP process unlike the\quasi-Beer-Lambert” hypothesis reported in a previous study. Thesedifferences were attributed to the differences in the exposure set upand the means by which the cure width data was computed. Studies showingthe variation of cure width with respect to light intensity,photoinitiator, and uv absorber concentrations were also presented.

(g) An algorithm for identifying floating islands in CAD files andgenerating support structures specific to the needs of the LAMP processwas presented. Previous approaches mostly worked on STL meshes and theyall produced straight supports aligned with the build direction thatgrow either from the base or from the geometry directly underneath thefloating island. These approaches cannot be applied in LAMP for thefabrication of integrally-cored turbine blade molds as it is impossibleto remove them post build. Hence a new approach wherein the floatingislands were connected to immediate surrounding geometries is presented.The potential for design for manufacturing specific to LAMP was alsodiscussed by means of evaluating the cooling performance of anillustrative support structure.

(h) Finally, novel cooling schemes that are currently impossible tofabricate using conventional manufacturing methods were presented. A fewnovel film cooling schemes have been analyzed using CFD and thermalanalysis techniques and their improvements over conventional simpleschemes were presented. This work gives a better appreciation of thepotential LAMP offers in opening up new doors of design opportunitiesfor building next-generation turbine blade designs.

FIGS. 75a and 75b illustrate a loss of build precision using a materialrecoating system having a single-edge recoater. In FIGS. 75a and 75b ,the material recoating system having a single-edge recoater may causestarvation or doming, which may result in loss of build precision. Inone example, for the first about ten to about twenty layers, a blade mayhave removed too much slurry and may form a crator shape in the slurryarea around a mold. Further, after about forty to about fifty layers, adome shape of slurry may be formed surrounding the mold parts. Thisdoming problem may get worse as, for instance, more layers are added,which may cause a build of a part to fail.

FIGS. 76a-76d illustrate one embodiment of a material recoating system7600 having a multiblade recoater in accordance with various aspectsdescribed herein. The system 7600 may be configured as described inFIGS. 76a-76d . Further, the system 7600 may be configured to addressthe starvation and doming issues described in FIGS. 75a 75b , which mayincrease build precision of a part.

FIGS. 77a-77c illustrate one embodiment of a screen printing-styleinking window pane in accordance with various aspects described herein.The screen printing-style inking window pane 7700 may be configured asdescribed in FIGS. 77a -77 c.

FIGS. 78a-78f illustrate one embodiment of a LAMP machine in accordancewith various aspects as described herein.

FIG. 79 illustrates one embodiment of a LAMP machine 7900 in accordancewith various aspects described herein.

FIG. 80 illustrates one embodiment of a LAMP machine 8000 in accordancewith various aspects described herein.

FIG. 81 illustrates one embodiment of a LAMP machine 8100 in accordancewith various aspects described herein.

FIG. 82 illustrates one embodiment of a LAMP machine material buildplatform 8200 in accordance with various aspects described herein.

FIG. 83 illustrates one embodiment of a LAMP machine material buildplatform 8300 in accordance with various aspects described herein.

FIG. 84 illustrates one embodiment of a LAMP machine material buildplatform substrate and substrate mount 8400 in accordance with variousaspects described herein.

FIG. 85 illustrates one embodiment of a LAMP machine material buildplatform substrate and substrate mount 8500 in accordance with variousaspects described herein.

FIG. 86 illustrates one embodiment of a LAMP machine material buildplatform substrate and substrate mount 8600 in accordance with variousaspects described herein.

FIG. 87 illustrates one embodiment of a LAMP machine material recoatingsystem 8700 in accordance with various aspects described herein.

FIG. 88 illustrates one embodiment of a LAMP machine material buildplatform seal system and material recoating system 8800 in accordancewith various aspects described herein.

FIG. 89 illustrates one embodiment of a LAMP machine material buildplatform seal system and material recoating system 8900 in accordancewith various aspects described herein.

FIG. 90 illustrates one embodiment of a LAMP machine material buildplatform seal system and material recoating system 9000 in accordancewith various aspects described herein.

FIG. 91 illustrates one embodiment of a LAMP machine material buildplatform seal system and material recoating system supply reservoir 9100in accordance with various aspects described herein.

FIG. 92 illustrates one embodiment of a LAMP machine material recoatingsystem supply reservoir and recoater 9200 in accordance with variousaspects described herein.

FIG. 93 illustrates one embodiment of a LAMP machine material recoatingsystem supply reservoir and recoater 9300 in accordance with variousaspects described herein.

FIG. 94 illustrates one embodiment of a LAMP machine material buildplatform seal, material recoating system supply reservoir and recoater9400 in accordance with various aspects described herein.

FIGS. 95a-95c illustrate an embodiment for employing a series of imagingheads that move concurrently across the surface of a resin in accordancewith various aspects as described herein. ULTRA-LAMP employs a series ofimaging heads as shown in FIGS. 95a-95c that may image the surface ofthe photocurable resin by concurrently moving over the photocurableresin's surface while exposing and curing patterns in the resin. FIG.95a demonstrates the ULTRA-LAMP in two staggered rows of imageprojection units. As shown by the arrows in the Figures, the projectionunits may sweep across the resin in opposite directions. The entiresurface of the resin may be thus patterned in a single pass, providingan increase in throughput of about 10× over current LAMP technology(which uses a serpentine scan of a single imaging head over the resin'ssurface.)

FIG. 96 illustrates an embodiment of for employing a two dimensionalarray of imaging heads to simultaneously pattern the surface of theresin in accordance with various aspects as described herein. In FIG.96, the technology may be applied in a FLASH-LAMP concept. FLASH-LAMP isillustrated in FIG. 96. FLASH-LAMP may use a two-dimensional array ofprojectors, all simultaneously projecting portions of a larger image butat high resolution. The entire area of the photocurable resin may bethus patterned in a single flash, or a few flashes with small indexingmovements of the array between flashes to cover areas of the resin notexposed in the previous flash. FLASH-LAMP may increase photoexposurethroughput dramatically by up to 50× over current LAMP technology.

The light source used in LAMP may be a high pressure mercury vapor lamp.The emission spectrum of the light source is shown in FIG. 97. There arethree distinct regions of emission from the light source, which are theI-line at 365 nm, H-line at 404.7 nm and G-line at 435.8 nm. For thislight source the G-line is the strongest spectral feature, followed bythe H-line and I-line, respectively. It is important to note that theprimary peak utilized for photopolymerization is the I-line, since thephotoinitiator utilized exhibits negligible absorption for the longerwavelengths.

Previous investigations conducted on grayscale exposures propose thatthe light intensity incident on the surface is effectively reduced. Thismay be characterized by a “grayscale factor,” g, which relates theaveraged grayscale light intensity to the “all white” light intensityand may be described by equation 3.1.

$\begin{matrix}{g = \frac{I_{gr}}{I_{o}}} & 3.1\end{matrix}$

Where I_(gr) is the averaged light intensity incident on the PCMSresulting from a half-toned grayscale exposure, and I_(o) is the lightintensity resulting from a full exposure, where every pixel on the DMDis turned to the on position. Intuitively, the grayscale factor could beassumed as being equal to the grayscale value of the image, i.e. thepercentage of white pixels in the designed image, G, and independent ofthe pixel distribution. This assumption was tested and the results areshown in FIG. 98.

The grayscale factor was determined using a photodetector provided bythe supplier of the optical scanning system. First, the current from afull projection was measured, which corresponds to the total light powerdelivered to the photodetector. The exposure area was held constantthroughout the experiment to give a direct relationship to the lightintensity. Next, the current resulting from projected grayscale imagesat different screening resolutions and grayscale values was measured.The screening process was accomplished using Harlequin RIP by GlobalGraphics, details may be found elsewhere. The screening technique usedwas Harlequin Dispersive Screening (HDS), which is a proprietaryscreening technique. Screening resolutions were varied from HDS superfine to HDS super coarse; here HDS super fine has the highest screeningresolution (1×1 pixel half-tone cells) and HDS has the lowest screeningresolution (4×4 half-tone cells). The grayscale factor was determined bydividing the grayscale current by the full exposure current. The errorassociated with this measurement technique was determined to be ±1%.Results show the validity of the assumption that the grayscale factor,g, is equivalent to the grayscale of the projected image, G. From FIG.98, the slope and intercept of the linear fit were found to be 1.004 and−0.003, respectively. Considering the error in the experimentalprocedure, it is reasonable to assume a slope of ˜1 and intercept of ˜0.From this experiment, it may be concluded that the average grayscalelight intensity incident on the surface of the PCMS, I_(gr), may beequal to the all white light intensity multiplied by the grayscale valueof the projected image, G. This result is summarized by equations 3.2and 3.3.

g=G  3.2

I _(gr) =I _(o) G  3.3

In addition, to the averaged effects of grayscale exposure, it is alsoimportant to consider the “true” distribution of light intensityprojected onto the PCMS. This was accomplished through the use of acharge-coupled device (CCD) BeamGage® Laser Beam Measurement systemsupplied by Ophir-Spiricon to measure the light intensity distribution.The spectral range of this profilometer is 190-1320 nm with ±1%linearity with power. The size of each pixel in the CCD is 4.4 μm, whichenabled sub-pixel level measurement of the SLM light output. Theprofilometer provides information about the optical profile in countsper second per pixel, which is analogous to light intensity. With thissetup, the light intensity distribution may be determined. However, dueto the lack of a calibration system, the actual magnitude of the lightintensity at each individual pixel cannot be directly determined. Thislimitation may be overcome by measuring all optical profiles underidentical conditions and camera settings to enable the determination oftrends in the light intensity distribution of different pixel patterns.

FIGS. 99a-99f show the light intensity distribution at the focal planeresulting from one pixel of the DMD being projected. The top panel showsthe light intensity plotted in the x-y plane, which is parallel with thePCMS surface, where reds correspond to high light intensity and bluescorrespond to low light intensity. Previous reports have described theintensity distribution for a single pixel as Gaussian.

$\begin{matrix}{{I\left( {x,y} \right)} = {I_{o}^{- \frac{({x^{2} + y^{2}})}{r^{2}}}}} & 3.4\end{matrix}$

where I_(o) is the peak light intensity and r is the Gaussian radius.

The bottom panel of FIG. 99a shows a plot of the cross-sectional profileof the projected pixel. The curve fit shown in the profile was obtainedthrough a two-dimensional Gaussian regression. From this regression, theGaussian radius was determined to be ˜8.3 μm, which is consistent with apixel resolution of 17 μm. The maximum measured value of intensity for asingle pixel exposure was 3600 counts/px-sec. The statistical error fromthe measurement was determined to be ±85 counts/px-sec and thehorizontal error bars show the dimensions of the CCD for which the datapoints were averaged. In order to better understand the light intensitydistributions resulting from SLM projections, additional pixel patternswere investigated. The figures FIGS. 99b-99f show the intensitydistributions and profiles of 2, 3, 4, 5 and 10 pixel lines,respectively. Sun et al. also suggest that projections of additionalpixels may be treated as the sum of Gaussian intensity distributions.Therefore, each distribution was regressed as a summation of 2, 3, 4, 5,and 10 two-dimensional Gaussian distributions, respectively. Theaveraged Gaussian radius from all the projections investigated was 8.6μm with a standard deviation of 1 μm. However, additional trends areobserved that a superposition of Gaussian distributions with a constantradius could not describe. In FIG. 99f , trends in the valleys may beseen, where a minimum is reached in the center of the 10 pixel line,which may be attributed to diffraction. This indicates that a moredetailed optical analysis is required. However, conventional techniquesfor modeling cure depth in stereolithography use the peak intensity ofthe laser to predict the cure depth. Therefore, for this study it issufficient to assess the trends in peak intensity resulting from thevarious intensity distributions. From these experiments, it may be seenthat the peak intensity remains constant with each of the linesinvestigated. The maximum intensity measured from the 10 pixel line was3683 counts/px-sec, which shows an increase of only ˜2% from that for asingle pixel projection.

The above results suggest that the pixel distribution may have littleeffect on the peak light intensity. In an effort to verify this, all thepixels of the SLM were projected. A profile of this exposure is shown inFIG. 100. The maximum intensity was found to be 3959 counts/px-sec,which indicates that the peak light intensity for single pixel exposuredecreases only ˜10% from that for a flood exposure. Additionally, FIG.100 shows the underlying complexity of the optical projection which isbeing neglected due to its negligible influence on the peak intensities.A periodic distribution in the intensity of the valleys is observed,which has a period of ˜220 μm and may be a result of diffraction.

When considering grayscale exposure, the material system could cureaccording to the local, averaged or an intermediate light intensityincident to the surface. Above, it was shown that the distribution ofprojected pixels does not significantly alter the maximum incident lightintensity. Therefore, if the cure depth resulting from grayscaleexposure is similar to the cure depth resulting from an all whiteexposure, then it may be concluded that the PCMS cures according to thelocal light intensity. However, if the cure depth resulting fromgrayscale exposure is lower than the cure depth of an all whiteexposure, then the curing behavior of the PCMS may be modeled as aneffective light intensity reduction. To investigate the response tograyscale exposure, cure depth measurements were conducted at a fixedexposure time and screening resolution and the grayscale was varied from30% to 90% white. The exposure time used was 600 ms and the screeningresolution was HDS super fine. The resulting films were homogenouslysmooth with no evidence of the pixel distribution utilized in thegrayscale exposure. The cure depth measurements in FIG. 101 clearly showthat in addition to the homogeneity of the films produced from grayscaleexposure, the cure depth decreases with a decrease in grayscale. Thisindicates that the light intensity has been effectively smoothed andreduced. From the findings in FIG. 101, it may be hypothesized thatgrayscale exposure causes the PCMS to cure as though the light intensitywas reduced in proportion to the grayscale value of the projected image.The validity and the limits of this hypothesis are the focus of thefollowing discussion.

Reports by Atencia et al. suggest that grayscale exposure with asufficiently high screening resolution results in an effective reductionin intensity which corresponds to the grayscale of the projected image.In order to relate the curing behavior to a grayscale light intensity,the effect of altering the “true” light intensity on the curingparameters may be determined. This may be accomplished through the useof UV neutral density (ND) filters, which act to uniformly attenuatelight intensity over a specified range of wavelength. UV-VIS ND filtersof a nominal optical density (OD) of 0.3 and 0.5 were purchased fromEdmund Optics to uniformly attenuate wavelengths from 200 nm to 700 nm.The transmission of the filters was measured using a technique similarto that used for determining the grayscale factor. First, an all whiteimage was projected onto the photodetector and the resulting current wasmeasured. Next, the ND filters 10202 were placed between the lightsource and the photodetector, and the current from an attenuated allwhite projection was measured. The ratio of these two currentmeasurements provides the transmission for each filter. The percenttransmitted for the 0.3 and 0.5 OD filters measured were 56% and 32%,which corresponds to a light intensity of 896 mW/cm² and 512 mW/cm²,respectively as compared to 1.6 W/cm² for unfiltered light. To exposethe PCMS to a reduced light intensity, the ND filter 10202 was placed ontop of the glass slide 10203 as shown in FIG. 102.

Cure depth measurements were conducted for each of the different lightintensities at multiple exposure times to develop working curves. Theexposure times were selected to investigate a consistent range of energydose for the different light intensities. FIG. 103 shows the resultingworking curves. The working curve resulting from an unfiltered lightintensity of 1.6 W/cm² is also shown for comparison. It may be seen thatthe cure depth for a constant energy dose increases when the lightintensity decreases. As a result, the cure depth from the highest sourceof light intensity resulted in the lowest cure depth. Consequently, thecritical energy decreases with a decrease in light intensity. While atfirst counterintuitive, it should be noted that for a constant energydose, the exposure time increase for a lower intensity, i.e. there ismore time for photopolymerization to proceed. From FIG. 103, it may alsobe seen that the slopes resulting from each light intensity curve remainconstant, which indicates that the resin sensitivity has littledependence on light intensity under these exposure conditions.

FIGS. 104a and 104b show a summary of the dependence of the criticalenergy and resin sensitivity on light intensity. The linear regressionof the critical energy, shown in FIG. 104a , resulted in the followingempirical relationship.

E _(c)=18.31*1+109  4.1

Where E_(c) is in units of mJ/cm², I is in units of W/cm² and the slopeis in units of ms. From this regression, R² was determined to be 0.999.This indicates that the critical energy has a strong linear dependencewith light intensity. Neither the Jacobs' equation (eq 2.9) nor theinhibitor equation (eq. 2.12) predicts this behavior. Rather, bothmodels assume that the curing parameters are constant for a givenmaterial system and independent of how the energy is delivered to thematerial system. Results from a linear regression of the resinsensitivity, shown in FIG. 104b , show a near horizontal slope,indicating that the resin sensitivity is relatively independent of lightintensity, which follows the Jacobs equation.

For grayscale exposure to be equivalent to an effective reduction inlight intensity proportional to the grayscale value of the projectedimage, trends observed with grayscale exposure may be similar to trendsobserved with true light intensity reduction, i.e. the critical energyshould have a strong linear dependence with the grayscale factor and theresin sensitivity should be relatively independent of the grayscalefactor. One method for evaluating the validity of the light intensityreduction hypothesis is to assume that the hypothesis is true andcompare the behavior of the curing parameters resulting from grayscaleexposure to the behavior observed for a true reduction in lightintensity. If the behaviors are similar, then the light intensityreduction model may be used to predict the curing characteristics ofgrayscale exposure. To test this hypothesis, numerous grayscale exposurecure depth experiments were conducted. Grayscale images from about 20%to about 90% white were designed at five different screeningresolutions: HDS super fine, fine, medium, coarse and super coarse.Working curves for each of the grayscale values and screeningresolutions were developed by measuring the cure depth at differentexposure times. The range of energy dose investigated under the lightintensity reduction hypothesis for each grayscale exposure was 320mJ/cm² to 1920 mJ/cm². FIG. 105 shows a sample of the working curvesresulting from grayscales of 50%, 40%, and 20% white and with HDS superfine screening.

From FIG. 105, trends similar to a true reduction in light intensity maybe seen. As the grayscale decreases, so does the critical energy. Thisis evidenced by a shift in the x-intercept and an increase in cure depthresulting from an equivalent energy dose. However, it may be noted thatthe resin sensitivity also shows a slight decrease with a decrease ingrayscale, which deviates from the light intensity reduction hypothesis.This is evidenced by a decrease in the slope with a decrease ingrayscale. These results suggest that the critical energy resulting fromgrayscale exposure may behave in a manner similar to a true reduction inlight intensity. However, additional phenomena may affect the resinsensitivity since its trends deviates from a true light intensityreduction.

Through the continued investigation of grayscale exposures, it was foundthat the curing parameters showed similar trends for each screeningresolution investigated. This is shown in FIGS. 106a-106j . Films ofuniform thickness were produced for all the HDS screening resolutionsinvestigated. At each grayscale value, similar values for the criticalenergy and resin sensitivity were obtained regardless of the screeningresolution. This indicates that the PCMS may behave in a similar mannerfor a range of screening resolutions and that the intensity reductionassumption is valid for each screening resolution. FIGS. 106a-106jquantify the trends observed in FIG. 105. It may be seen that a linearregression of the critical energy accurately describes the variationwith grayscale, which is evidenced by the high R² values. This indicatesthat the critical energy for grayscale exposure at different screeningresolutions varies in a manner similar to its variation with uniformlight intensity. Additionally, a linear regression of non-horizontalslope accurately described the resin sensitivity, which deviates fromthe trends observed for varying light intensity. Since the trends inresin sensitivity and critical energy are within the error determinedfor each screening resolution, the results may be combined to obtain abetter regression of the trends in curing parameters, which may helpprovide a better understanding of the curing characteristics whenhomogenous films are produced from grayscale exposure.

The trends in curing parameters from homogenous grayscale exposure areshown in FIGS. 107a and 107b . In these figures, the image grayscale wasconverted to its effective intensity in order to compare the resultswith the critical energies obtained from a true reduction in lightintensity. Both the critical energies from grayscale exposure and trueintensity measurements were plotted. From FIGS. 107a and 107b , it maybe seen that the grayscale exposure critical energies are within theerror of the critical energies obtained from true intensitymeasurements. This shows that the critical energy resulting fromgrayscale exposure behaves as a true reduction in light intensity. Theregression obtained for the influence of grayscale exposure on thecritical energy was:

E _(c)=19.6*I+103.7  4.2

Here, I was obtained by multiplying the all white light intensity by thegrayscale of the image. The R² value obtained for this regression was0.92, which indicates that the regression is a good fit of the data.Also, it may be noted that the slope with light intensity varies by only1.3 mJ/W and the critical energy at zero light intensity varies by only5.3 mJ/cm², which is within the average confidence interval of 5.6mJ/cm² obtained during the grayscale exposure measurements. In additionto E_(c), the resin sensitivity also shows a strong linear dependence onlight intensity.

D _(p)=11.3*I+194.8  4.3

From this regression, R² was determined to be 0.94, which shows that theregression is an adequate representation of the influence of grayscalelight intensity on the resin sensitivity.

In the present grayscale investigation, only the screening resolutionsresulting in a homogenous film have been considered. However,intuitively if sufficiently large collections of exposed and unexposedpixels are projected onto the PCMS, film homogeneity will be lost andregions of cure depth with all white exposure will develop accompaniedwith regions of uncured resin. To date, few reports have characterizedthe cure depth within the homogenous transition. However, the homogenoustransition is a region of interest in the investigation of methods tomitigate polymerization shrinkage stress. Reports by Ganahl show thatfor a given material system, there exist optimal dimensions of linewidth and line spacing to reduce the stress in a photopolymerized film.It may also be noted that the films generated by Ganahl were notuniform, nor were cured regions completely isolated from each other.Rather, the film contained regions of a larger cure depth connected byregions of partially cured resin with a lower cure depth. Thiscorresponds to the homogenous transition, which corresponds todimensions of exposed and unexposed regions for which the materialsystem cannot create distinct regions of cured polymer separated bydistinct regions of uncured monomer. This spatial modulation of thedegree of conversion reduced shrinkage stress in the material systeminvestigated by Ganahl, which indicates that it may reduce shrinkagestress in the PCMS used in LAMP.

In order to incorporate features containing dimensions within thehomogenous transition in multilayer builds, the cure depth must bepredicted to ensure proper binding to the previous layer. Theinvestigation of the homogenous transition was accomplished through theselection of one grayscale value. Also, the screening technique wasconverted to a well-defined pattern in order to easily extractdimensional information. The pattern chosen was a “checkerboard,” whichis shown in FIG. 108.

The checkerboard pattern consists of alternating squares of exposed andunexposed regions. To investigate the influence of screening resolution,the length of the square primitive was successively increased. The rangeof square lengths investigated was from about 1 pixel to about 80pixels, which corresponds to about 17 μm to about 1360 μm. Eachcheckerboard pattern has an image grayscale value of 50%. However, asthe screening resolution decreases, the image visually appears less grayand more as a pattern of distinct black and white squares. Similarly, asthe screening resolution decreases, the light intensity reductionassumption of grayscale exposure breaks down.

Images in FIGS. 109a-109d show the homogenous transition for a 600 msexposure. It may be seen in FIG. 109a that a checkerboard exposure witha square length of 17 μm results in a film with uniform thickness.However, when the square length reaches 85 μm in FIG. 109b ,inhomogeneities in the film thickness are observed. This represents theonset of the homogenous transition. FIGS. 109c and 109d depict thecontinued deviation from homogeneity for square lengths of 170 μm and255 μm. As the homogenous transition progresses, the cure depth of theexposed regions increases and that of the unexposed regions decreases.

When characterizing the effect of the homogenous transition on the curedepth, it may be seen in FIG. 110 that the homogenous transitionseparates two regions of constant and homogenous cure depth. The regionwith lower cure depth occurs when square length of the checkerboardexposure pattern is small, which corresponds to grayscale exposure. Theregion with a higher constant cure depth is from an all white exposure.These two regions are separated by the homogenous transition where thecure depth increases as the square length of the checkerboard increasesfor a given exposure time. One interesting aspect of the results shownin FIG. 110 is the shifting of the homogenous transition to the rightwith an increase in exposure time. The center of the sigmoid regressionincreases with an increase in exposure time to larger square lengths.The center of the 200 ms exposure time was at a square length of about172 μm, while the center of the 900 ms exposure was at a square lengthof about 330 μm. From these cure depth measurements, it was observedthat the average square length range of the homogenous transition wasfrom about 100 μm to 450 μm.

This time dependent aspect of the homogenous transition is furtherdemonstrated in FIGS. 111a-111d , which shows a checkerboard exposurewith a square length of about 170 μm. At an exposure time of 250 ms, itis clear that the film is not homogenous. The side length was measuredto be 156 μm. As the exposure time increases, the side length increasesto 173 μm at 400 ms, and 203 μm at 800 ms. However, at a sufficientlyhigh exposure time of 2400 ms, a homogenous film of uniform thickness isdeveloped.

These results show the dimensional and exposure time limits for thegrayscale intensity assumption as well as the limits for an all whiteintensity assumption. For the cure depth to increase with a constantexposure time, the effective intensity must also increase. As a result,the intensity within the homogenous transition is not well defined anddepends on the separation length as well as the size of exposed regions.Consequently, the Jacobs equation cannot directly be used because thelight intensity cannot be determined. However, in order to obtain apredictive cure depth model, the Jacobs equation may be modified toignore the light intensity and consider only the exposure time, which isshown in equations 4.4-4.7.

$\begin{matrix}{E = {I*t}} & 4.4 \\{E_{c} = {I*t_{c}}} & 4.5 \\{C_{d} = {{D_{p}\ln \frac{E}{E_{c}}} = {D_{p}\ln \frac{I*t}{I*t_{c}}}}} & 4.6 \\{C_{d} = {D_{p}\ln \frac{t}{t_{c}}}} & 4.7\end{matrix}$

Here, D_(p) is equivalent to the resin sensitivity in the unmodifiedJacobs equation, t is the exposure time, t_(c) is the critical exposuretime, and I is the maximum effective light intensity. This equation maybe applicable to the light source used. However, it may accuratelypredict the cure depth, which allows the implementation of exposurepatterns within the homogenous transition in LAMP. The critical exposuretime, t_(c), may be determined by the same method use to determineE_(c). Exposure time working curves of selected checkerboard squarelengths are shown in FIG. 112. From these results, it may be seen thatas the square length of the checkerboard pattern increases, the slopes(resin sensitivity) first decrease, reach a minimum and then increase. Asimilar pattern is also demonstrated in the x-intercepts (criticalexposure time). Both minimums in the resin sensitivity and the criticalexposure time occur at a similar checkerboard pattern.

These phenomena are investigated further in FIGS. 113a and 113b where asummary of the curing parameters obtained within the homogenoustransition are provided. When the square length is about 85 μm andlower, the curing parameters are constant, indicating that grayscalelight intensity assumptions may be made. Also, when the square length isabout 1360 μm and greater, the curing parameters reach all whiteintensity values and a full intensity assumption may be made toaccurately predict the cure depth. It may be seen that within thetransition from grayscale exposure to all white exposure a minimumexists in both the critical exposure time and resin sensitivity at asquare length of 425 μm. It is interesting to note that at thisscreening resolution, curing will begin sooner than an all whiteexposure. However, due to the minimum in resin sensitivity, the curedepth growth rate is much slower than an all white exposure.

Two factors may influence the cure depth resulting from projectedgrayscale images. These are the grayscale value of the image and thescreening resolution used to convert the image to a distribution ofblack and white pixels. Based on these results, three distinct exposuretypes emerge: all white exposure, homogenous transition exposure, andgrayscale exposure

A standard method for predicting the cure depth is dependent on thetotal energy dose and is independent of light intensity. However,results described in previous discussions above distinctly contradictthis assessment for a reduction in uniform light intensity as well asgrayscale light intensity. In the case of uniform light intensityreduction, it was determined that the manner in which the energy isdelivered to the PCMS effects the critical energy, wherein increasinglight intensity increases the critical energy. This effect was alsoobserved with grayscale exposures and as a result, concepts used topredict and explain the critical energy variation with uniform lightintensity can also be used to predict the critical energy variation withgrayscale light intensity. Recently, the light intensity dependence ofthe critical energy has been recognized and models have been developedin an effort to describe this phenomena. When the intensity of lightincident on the PCMS is increased, the rate of initiation of primaryradicals is directly affected, which is shown in Equation 2.2. If thelight intensity is increased, more primary radicals are generated forpolymerization. A higher rate of initiation will increase the rate ofpolymer chain propagation.

$\begin{matrix}{R_{p} = {{k_{p}\lbrack M\rbrack}\left( \frac{R_{i}}{2k_{t}} \right)^{\frac{1}{2}}}} & 5.1\end{matrix}$

Where k_(p) and k_(t) are the rate constants of propagation andtermination, which are considered material properties independent of theinitiation rate. Therefore, the variation in cure depth with lightintensity can be considered a result of competition between initiation,propagation and termination reaction rates. This concept was the basisfor a simplified radical depletion model developed by Halloran et al.Conceptually, if the radical initiation rate is high due to a high lightintensity and compared to k_(p), an excess of free radicals will arisein the PCMS and the potential for radical depletion reactions such asrecombination, trapping and de-excitation will increase. As a result, aportion of the generated radicals will not contribute to polymerization.Therefore, at higher light intensities, more photons (higher energydose) are required to develop an equivalent cure depth. These conceptscan be expressed by Equation 5.2.

E _(c)(I)=E _(c,DE) +E _(c,excess)(I)  5.2

Where E_(c,DE) is the “dose equivalent” critical energy, whichcorresponds to the range of light intensities where the critical energyis constant and independent of light intensity and E_(c,excess)(I) isthe increase in critical energy resulting from exposure to lightintensities greater than the dose equivalent intensity range. The doseequivalent critical energy can be predicted by the inhibitor exhaustionmodel in Equation 2.12. Since HDDA is a fast reacting monomer, it wasfound that at low light intensities, the PCMS shows dose equivalence.This is expressed by Equation 5.3 and in Equation 5.4 an expression fora minimum light intensity was proposed.

$\begin{matrix}{E_{c} = {E_{c,{DE}}\left( {1 + \frac{I}{I_{\min}}} \right)}} & 5.3 \\{I_{\min} = {{k_{p}\lbrack M\rbrack}{fhv}}} & 5.4\end{matrix}$

-   -   Where I_(min) is the transition light intensity for describing        dose equivalence, k_(p) is the propagation rate constant, [M] is        the monomer concentration, f is a proportionality factor, h is        Planck's constant and v is the frequency of the incident light.        If the light intensity is lower than I_(min) the system behaves        independent of light intensity and if the light intensity is        greater than I_(min) the system depends on the light intensity.        The change in critical energy with light intensity was proposed        to be described by Equation 5.5.

$\begin{matrix}{\frac{\delta \; E_{c}}{\delta \; I} = {\left( {1 - \Phi} \right)\left( \frac{{\gamma_{INH}c_{INH}} + {\gamma_{A}c_{A}}}{\Omega \; {{fk}_{p}\lbrack M\rbrack}ɛ_{p}} \right)\left( \frac{1}{c_{p}} \right)}} & {.5}\end{matrix}$

Where γ_(INH) and γ_(A) is the effectiveness of the inhibitors andabsorbers, c_(INH) and c_(A) are the concentrations of inhibitors andabsorbers, and f is a proportionality factor. From this equation, it ispredicted that the change in critical energy will be inverselyproportional to photoinitiator concentration and directly proportionalto inhibitor and absorber concentration. However, for a selectedformulation, the change in critical energy is expected to be linear. Thelinear trends found for the critical energy with grayscale and uniformlight intensity suggest that this model can be used to predict thedependence of critical energy on light intensity. However, it should benoted that the predicted values deviate from the measured values. Valuesfor the change in critical energy with light intensity presented byHalloran et al. were between 0.08 mJ/mW and 0.1 mJ/mW, which contrastwith the values of 0.02 mJ/mW obtained in this study shown in Equation4.2. This indicates that there may be additional effects contributing tothe light intensity dependence of the critical energy. Some additionalfactors which could be considered are the variation in the range ofinvestigated exposure dose and the use of different light sources. Thecure depths measured as described in previous discussions above were athigher energy doses than those used by Halloran et al. Therefore,differences may have developed due to the different stages ofphotopolymerization. At low exposure dose, the PCMS is in the initiationphase whereas at a higher dose, polymerization is in the propagation andtermination stages. As a result, factors such as reduced mobility ofpropagating chains may influence the dependence on light intensity. Theuse of different light sources may alter the efficiency of initiation ofprimary radicals. A light source with a lower efficiency of initiatingprimary radicals may decrease radical depletion reactions and result inless variation with light intensity.

When investigating the influence of true light intensity variation onthe resin sensitivity, it was found to behave independently of lightintensity, which is consistent with Halloran's results. However, it canbe seen in figures described above that grayscale exposure produces avariation in resin sensitivity, where the resin sensitivity decreaseswith a decrease in grayscale light intensity. This shows that while thecritical energy can be treated as a function of true reduction in lightintensity, the resin sensitivity may not. Due to the complexityassociated with light scattering in highly loaded ceramic suspensions,numerical simulations may be required to fully investigate thisphenomenon. However, a potential explanation for this effect may befound in the differences of the exposure technique. When a uniformlydistributed light intensity is projected onto the PCMS, absorption canonly develop vertically. This is contrasted with grayscale exposure,where incident light intensity is not uniform. As a result ofscattering, absorption may be distributed both with depth and width.When the percentage of white pixels is high in the projected image, mostof the absorption is with depth. However, as the grayscale valuedecreases, the percentage of regions with lateral absorption increases.This increase in lateral absorption may reduce the vertical absorption.Since the working curve measures only the cure depth, the determinationof resin sensitivity is of vertical absorption. This may be the basisfor scattering effects producing a dependence of resin sensitivity onthe grayscale value of the projected image.

When the screening resolution of a grayscale image projected onto thePCMS is within the homogenous transition, neither the grayscale lightintensity nor the all white light intensity can accurately predict theresulting cure depth. When considering exposure features within thislength scale, it is important to consider how grayscale exposure maydevelop from fully exposed regions separated by unexposed regions. Indiscussions above, it was shown that the peak intensity from a one pixelprojection is ˜90% of the peak intensity resulting from an all whiteprojection where every pixel of the DMD was switched on. Similarly, thepeak intensity resulting from the checkerboard exposure pattern wasmeasured and it was verified to have peak light intensities within ˜90%of the fully projected intensity as well.

As a result, the prediction of the cure depth from grayscale exposuredeviates from the common method for predicting the cure depth instereolithography, which uses the peak intensity of the laser beam topredict the depth of cure. In contrast, grayscale exposure curesaccording to the grayscale value of the projected image, whichcorresponds to the average light intensity incident to the PCMS. Whenthe screening resolution enters the homogenous transition, the PCMSbegins to deviate from this averaging effect. This indicates that thePCMS has some critical dimension for which the light intensity isdistributed or averaged. Conceptually, it may be interpreted that thematerial system has its own “pixel,” where the power input to the“pixel” divided by its area is the resultant light intensity that causescuring in the PCMS. It can be hypothesized that for scattering systems,the dimensions of the material system's pixel are determined by thescattering length. Due to ceramic particle loading, light may bescattered instead of being absorbed by the photoinitiator. As a result,the light intensity is spread laterally to unexposed regions. To predictthe scattering length and subsequent lateral resolution of the PCMS, theresin sensitivity equation can be considered, which is shown in Equation2.11 and can be rearranged to solve for scattering length.

$\begin{matrix}{I_{sc} = \left( {\frac{1}{D_{p}} - {\left( {1 - \Phi} \right)\left( {{c_{p}ɛ_{p}} + {c_{A}ɛ_{A}}} \right)}} \right)^{- 1}} & {.6}\end{matrix}$

This equation enables the prediction of the light intensity for whichthe PCMS cures for any length scale. FIG. 114 shows a schematic for howthe light intensity within the PCMS can be predicted by the “scatteringlength pixelation model.” In this model, the PCMS resolution is definedas the scattering length, which translates into the radius of the PCMS“pixel.” The light intensity input into this pixel is averaged over thepixel area to obtain an effective light intensity at the pixel's center.Then the pixel's center is translated an incremental distance from theprevious location and the intensity is averaged over the scatteringlength pixel area for the new center. This process is repeated over theentire exposure area and acts to smooth out the light intensity byincreasing the light intensity in unexposed regions and decreasing thelight intensity in exposed regions.

In order to properly predict the light intensity, the correct resinsensitivity is be selected to determine the proper scattering length.During homogenous transition exposure the resin sensitivity varies withthe length of the square length in the checkerboard pattern. Thisvariation may be described by the same mechanisms proposed to explainthe decrease in resin sensitivity observed in grayscale exposure. As theseparation between exposed regions increases from grayscale exposure,more absorption is permitted to occur laterally due to scattering, whichresults in a decrease in D_(p). However, as the pixel distributionapproaches near all white exposure, lateral absorption is reduced, andthe vertical absorption increases to the all white exposure resinsensitivity. Therefore, to predict the cure depth within homogenoustransition exposure, the resin sensitivity values for each particularscreening resolution are used.

In addition to selecting the proper resin sensitivity input for Equation5.6, the molar extinction coefficients should be known. Estimates ofthese values can be obtained from the literature. A summary of theparameters used to predict the light intensity distribution for variousscreening resolutions are shown in the tables below. The pixel averagingtechnique shown in FIG. 114 was used to predict the light intensitydistribution experienced by the PCMS resulting from homogenoustransition exposure.

TABLE Summary of the properties used in the calculation of scatteringlength based on equation 5.6. Material properties used for predictingthe scattering length ε_(p) 80 (L/mol-cm) [43] ε_(A) 2300 c_(p) 0.102(mol/L) Chapter 2 c_(A) 0.002 (Φ) .55 vol % Scattering length forinvestigated checkerboard screening resolutions Square length (μm) D_(p)(μm) l_(sc) (μm)  17 216.6 247 170 199.9 226 340 186.6 209 510 200.8 227

Results from these simulations are shown for selected checkerboardscreening resolutions of 17 μm, 170 μm, 340 μm, and 510 μm in FIGS.115a-115d . Initially, when the square length of the checkerboard imageis small, the result is a uniform reduction in light intensity at thegrayscale value of the projected image, which for the checkerboardexposure pattern is 50%. As the square length of the checkerboardpattern increases the light intensity increases in the exposed regionsand decreases in the unexposed regions. Once the square length issufficiently large the light intensity reaches the all white exposureintensity.

From FIGS. 115a-115d , it can be seen that when the square lengthapproaches 510 μm, the peak light intensity reaches the all whiteexposure intensity. This simulated result has a strong experimentalvalidation, which was shown in figures previously described above wherethe cure depth plateaus with an increasing square length. This is aresult of reaching the peak all white light intensity. While lightscattering in a highly loaded ceramic suspension is complicated, thisscattering length pixelation model indicates that it may provide anaccurate estimate of the scattered light intensity distribution incidenton the PCMS.

When considering experimental cure depth measurements, the cure depthwill be determined by the maximum thickness of the cured sample, whichwill result from the maximum incident light intensity experienced by thePCMS. From the simulations in FIGS. 115a-115d , the maximum lightintensity was determined and the cure depth is predicted by Equation 5.7as follows

$\begin{matrix}{C_{d,\max} = {D_{p,{sr}}\ln \frac{I_{\max}}{E_{c}}}} & 5.7\end{matrix}$

Where D_(p,sr) is the resin sensitivity for the selected screeningresolution, E_(c)(I) is the intensity dependent critical energy shown inEquation 4.2, I_(max) is the maximum light intensity obtained from thesimulations, and t is the exposure time. Results from these simulationsare compared with the experimental working curves in FIGS. 116a-116d .It can be seen that the scattering length pixel model accuratelypredicts the maximum light intensity. The R² values obtained from thesesimulations ranged from 0.89 to 0.99. Due to these high R² values, thisindicates that the scattering length pixelation model accuratelysimplifies the complex phenomena of light scattering in ceramic loadedsuspensions. In addition, this model introduces new length scales whichcan be used in LAMP to fabricate features within the homogenoustransition. However, a possible limitation of the model may be the needto determine the effective resin sensitivity for the target screeningresolution. This possible limitation may be overcome by the developmentof a method to approximate the resin sensitivity or scattering lengthwithin the homogenous transition.

In addition to homogenous transition exposure transforming the lightintensity experienced by the PCMS, it was also shown in figurespreviously described above that the homogenous transition is dependenton exposure time. This can be attributed to cure width growth. While thelight intensity distribution experienced by the PCMS can be assumed tobe independent of exposure time, the cure width from regions of highlight intensity will grow into regions of lower light intensity, whichcan be described by an adapted Jacobs' cure width equation, which isshown in Equation 5.8.

$\begin{matrix}{C_{w} = {B\sqrt{\ln \frac{I_{\max}t}{E_{c}(I)}}}} & 5.8\end{matrix}$

Where C_(w) is the cure width and B is the diameter of the PCMS pixel,which is B=2l_(sc). As the exposure time increases, eventually the curewidth will overlap with the cure width from an adjacent projectedregion. Consequently, screening resolutions within the homogenoustransition at low exposure times may be homogenous layers with uniformthickness at high exposure times. This is demonstrated in figuresdescribed above for a square length of 170 μm.

Mechanisms of grayscale and homogenous transition exposure weredescribed, and the causes for the variation of the curing parameterswith grayscale light intensity were investigated. It was concluded thatthe critical energy behaves equivalently to trends for variation inuniform light intensity, which may be adequately predicted by theradical depletion model presented by Halloran. The critical energy wasfound to vary linearly with light intensity which is predicted in theradical depletion model. However, the magnitude of the variation was notaccurately predicted, which may be related to differences in the energydose range investigated as well as differences in the light source. Theresin sensitivity was found to decrease with a decrease in grayscalelight intensity, which deviates from the behavior for uniform lightintensity variation. This was proposed to be related to the differencesin the exposure method, where the screening technique used in grayscaleexposure enables lateral scattering and subsequent absorption, which mayreduce vertical absorption measured by cure depth working curves. Indiscussions above, the mechanisms behind homogenous transition exposurewere described and the “scattering length pixelation model” was proposedto predict the light intensity experienced by the PCMS during homogenoustransition exposure. The model treats the scattering length as thecritical resolution of the material system, where the light intensity ofthe “pixel center” is obtained by the total incident power within thescattering length divided by the scattering length area. Theeffectiveness of the model was assessed at selected checkerboardexposure patterns and it was found to predict the cure depth to a highlevel of accuracy. The time dependence of the homogenous transition wasdiscussed and it was proposed to be related to the cure width where thediameter of the exposure is twice the scattering length.

In some embodiments, LAMP may be used to fabricate unsupportedgeometries and to reduce defects which arise during BBO due to internalstresses resulting from polymerization shrinkage stress. Discussed beloware trends observed in the degree of conversion due to grayscaleexposure, wherein the effect of grayscale exposure and screeningresolution are presented and compared to an all white exposure. Alldiscussed is a framework for utilizing grayscale exposure to fabricateunsupported features. The effectiveness of generating grayscale supportstructures (GSS) is also presented and the results are discussed. Aframework for reducing defects in LAMP using grayscale exposure isdiscussed and the effectiveness of this framework is presented and theinfluence of grayscale on other types of defects is discussed.

In some embodiments, it may be desirable to develop a cure depth modelfor the incorporation of grayscale exposure in LAMP. It may enable, forexample, the prediction of exposure dose or exposure time to generatethe desired cure depth to ensure adhesion to the previous layer.However, the cure depth model provides no information on the degree ofpolymerization, which is useful for making decisions regarding whichgrayscales are appropriate to address the challenges facing LAMP. FTIRmeasurements, on the other hand, may provide information about thedegree of monomer conversion, which is directly related to the degree ofpolymerization. For the fabrication of unsupported geometries, forexample, grayscale exposure may be applied to the surrounding regions inorder to provide a GSS, where a particular degree of conversion willcorrespond to an appropriate support structure. Additionally, volumetricshrinkage and shrinkage stress information may be obtained from degreeof conversion and rate of conversion measurements.

When considering the influence of grayscale exposure on the degree ofconversion, two factors may play an important role in modulating thedegree of conversion between an all white exposure, i.e., (1) thegrayscale value and (2) the screening resolution of the projected image.

First, the influence of homogenous grayscale exposure may beinvestigated. The degree of conversion may then be calculated from theresulting FTIR spectra according to equation 2.13. The grayscale valuesinvestigated were 20%, 40%, 60% and 80%. Also, the degree of conversionfor an all white, 100% exposure was investigated to serve as areference. The degree of conversion was measured for each grayscalevalue at various exposure times so as to maintain a constant range ofenergy dose. Results of the degree of conversion measurements are shownin FIGS. 117a and 117b . Reports by Ogliari, et al., show that thedegree of conversion measurements may be regressed by Hill's threeparameter nonlinear regression with R² values of 0.99.¹ Likewise, eachgrayscale exposure was regressed to Hill's equation and R² valuesgreater than 0.98 were obtained. As a result, these curves may be usedto gain an understanding of the trends and rates of polymerization. ¹F.A. Ogliari, C. Ely, G. S. Lima, M. C. M. Conde, C. L. Petzhold, F. F.Demarco, and E. Piva, “Onium salt reduces the inhibitory polymerizationeffect from an organic solvent in a model dental adhesive resin,”Journal of Biomedical Materials Research Part B: Applied Biomaterials,vol. 86B, pp. 113-118, 2008.

Photopolymerization may be described in three phases, which areinitiation, propagation and termination.² These stages are observed inFIG. 117. Initially, at low exposure times, the degree of conversionslowly increases, which is due primarily to the limited mobility ofinitiated radical species. After initiation, the monomer is rapidlyconverted to increase the molecular weight and form a cross-linkedpolymer network, which occurs during the propagation stage. Thetermination stage experiences autodeceleration, where chain propagationbecomes diffusion controlled and the mobility of propagating radicalchains is reduced. In the use on multifunctional acrylates such as HDDA,this prevents the final conversion from reaching 100%. As shown, thedegree of conversion plateaus at approximately 82%. This indicates thatresidual monomer is retained in the PCMS. ²C. Decker, “Photoinitiatedcrosslinking polymerisation,” Progress in Polymer Science, vol. 21, pp.593-650, 1996.

From FIGS. 117a and 117b , it may be seen that grayscale exposureprolongs the initiation and propagation stages. This may be seen from alower degree of conversion for a lower grayscale at a given exposuredose when the exposure time is lower than 2000 ms. However, grayscaleexposure does not change the final conversion of the polymer; rather,grayscale primarily affects the rates of polymerization. This is shownin the bottom panel of FIGS. 117a and 117b , where the derivatives ofthe regressed models are plotted. As shown, as the grayscale valuedecreases, so does the maximum rate of monomer conversion. Additionally,the maximum rate of polymerization is delayed to higher exposure times,with the exception of 80%, which occurs at an exposure time similar to100% white. This indicates that an 80% grayscale exposure does notsignificantly modulate the degree of conversion from an all whiteexposure. However, when the grayscale value is lower than 80% white, thereduction in polymerization rate is increased. Additionally, it shouldbe noted that the maximum rate of polymerization is shifted to higherexposure times for grayscale values of 60% or less.

In addition to considering grayscales within the homogenous region, itis also necessary to characterize the degree of conversion resultingfrom grayscale exposure within the homogenous transition, which is shownin FIG. 118. To characterize the effect of the homogenous transition onthe degree of conversion, an exposure time of 600 ms and a grayscalevalue of 50% white were examined. The checkerboard pattern was used asthe screening technique and the square length of the primitives wasvaried from 17 μm to 1360 μm. It may be seen that there exists a minimumin the degree of conversion as the square lengths increase through thehomogenous transition, which follows a similar trend to that seen in theresin sensitivity in FIGS. 113a and 113 b.

Results from the dependence of the degree of conversion on the screeningresolution may be separated into three regions: (1) grayscale exposure,(2) homogenous transition exposure, and (3) all white exposure. Withinthe grayscale exposure region, the degree of conversion is found to beconstant. A constant degree of conversion is obtained since anyscreening resolution with dimensions smaller than the scattering lengthacts to effectively reduce the light intensity to the grayscale of theprojected image. When the square length is within the homogenoustransition, on the other hand, the degree of conversion drasticallydecreases. This is anomalous behavior, since the homogenous transitionis a result of grayscale light intensity increasing to all white lightintensity.

Because of this behavior of the homogenous transition, it was expectedthat the degree of conversion would also increase with the transitionfrom grayscale exposure to all white exposure. However, while the lightintensity is increasing in the exposed regions of the checkerboardpattern, the light intensity is decreasing in the unexposed regions.Consequently, residual and partially polymerized monomer becomes trappedbetween the exposed regions within the film.

It is important to note that FTIR-ATR provides an averaged spectrum ofthe conditions of the investigated surface. Therefore, the averagedegree of conversion decreases upon entering the homogenous transitionfrom the grayscale exposure region. However, the actual state of theinvestigated layer consists of regions with high and low degree ofconversion, which corresponds to the exposed and unexposed regions,respectively. As the square lengths increase and exit the homogenoustransition the degree of conversion increases and exceeds the degree ofconversion obtained from grayscale exposure.

This gradual increase in degree of conversion is related to theincreased ability to remove residual monomer from the unexposed holes inthe film. As the square length continues to increase, the degree ofconversion eventually reaches a constant value. This region correspondsto the all white exposure region and the degree of conversion measuredfor this region is consistent with the degree of conversion measured forthe 100% white exposure sample shown in FIGS. 117a and 117 b.

When considering grayscale exposure as a technique for constructing GSSin LAMP, three aspects may be considered: (1) the GSS is preferablystrong enough to survive material recoating, (2) the GSS is preferablyrigid enough to maintain the spatial location and geometry of theunsupported feature, and (3) the GSS should be easily removed bydevelopment with an appropriate solvent, for example, after completionof the build.

Each of these aspects may be related to the degree of conversion. As thedegree of conversion increases, both the viscosity and hardnessincrease.³ For the grayscale layer to survive material recoating, forexample, the degree of conversion is preferably sufficiently high—i.e.,the viscosity and hardness should reach a predetermined value—to preventthe partially polymerized region from being removed or shifted from theintended location. Similarly, the degree of conversion should reach apredetermined value to ensure accuracy of the target feature. However,to contrast the requirements of a sufficiently high degree ofconversion, the viscosity and hardness are preferably low enough to beeasily removed after completion of the build to fabricate only theintended feature. The result of these two competing requirements is atarget window for the degree of conversion for the successfulfabrication of GSS. Additionally, it is possible that the degree ofconversion required to survive material recoating may be higher than thedegree of conversion which provides an easy removal of the GSS after thefabrication is complete. F. Jack L, “Correlation between hardness anddegree of conversion during the setting reaction of unfilled dentalrestorative resins,” Dental Materials, vol. 1, pp. 11-14, 1985; R. P.Slopek, “In-situ Monitoring of the Mechanical Properties during thephotopolymerization of acrylate resins using particle trackingmicrorheology,” Ph.D. Thesis, Chemical and Biomolecular Engineering,Georgia Institute of Technology, Atlanta, 2008.

Typically, but not always, a constant exposure time is used in LAMP forphotopolymerizing individual layers throughout an entire build, whichmay be determined by calculating the exposure time required to produce acure depth of approximately 135 μm-155 μm (depending on the polymerused). A cure depth larger than the layer thickness may be used toensure proper adhesion to the previous layer. These exposure timestypically range from approximately 120 ms to 180 ms, again based on thematerial formulation and age of the light source.

As a result, this provides an exposure time range for which the curedepth and degree of conversion from grayscale exposure may beconsidered. Both the cure depth model and degree of conversionmeasurements may be used to determine the appropriate range of grayscalevalues to investigate for GSS fabrication. If the critical energy dosefor a selected grayscale value is greater than the grayscale energydose, then no curing will occur, which indicates that this grayscale isnot appropriate for GSS. However, if grayscale exposure produces asuitable cure depth (e.g., 100 μm or greater), then the GSS may be notbe easily removed after the build is complete. Based on this rationale,the appropriate grayscale range for GSS may be estimated. In someembodiments, the range may be between approximately 46% and 82% byincorporating equations 4.2 and 4.3 into Jacobs' equation.

$\begin{matrix}{C_{d} = {{D_{p}(I)}\ln \frac{E}{E_{c}(t)}}} & 6.1 \\{C_{d} = {\left( {{11.3*I_{o}*g} + 194.8} \right)\ln \frac{I_{0}*g*t}{{19.6*I*g} + 103.7}}} & 6.2\end{matrix}$

In addition to considering the cure depth equation, the degree ofconversion may also aid in the selection of an appropriate grayscale forGSS. From FIGS. 117a and 117b it may be seen that at an exposure time of˜170 ms, the degree of conversion is ˜14%. As a result, the grayscaleused should preferably produce a degree of conversion lower than that ofthe all white exposure. Grayscale values near 80%, for example, producea degree of conversion similar to that for an all white exposure, whichtends to indicate that an 80% grayscale value will produce mechanicalproperties similar to an all white exposure during a build.Consequently, a grayscale value of 80% is likely not appropriate forGSS.

From FIGS. 117a and 117b it may be seen that grayscale values of 60% andbelow produce a degree of conversion notably lower (˜5%) than an allwhite exposure. Based on these findings accompanied with cure depthpredictions, the range of grayscales appropriate for GSS fabrication inLAMP may be predicted. In some embodiments, the range may be betweenapproximately 46% and 60%.

It should be noted that a degree of conversion of 14% is below the gelpoint, which is defined as the degree of conversion where the maximumrate of polymerization is reached.⁴ This indicates that when a layer isfirst exposed to UV light in LAMP, the viscosity and modulus are lowcompared to the completed airfoil mold. The maximum rate ofpolymerization for an all white exposure was shown to occur at ˜27%±2%,which is consistent with the literature. Since the green body moldsresulting from LAMP retain accurate geometries, this indicates that muchof the photopolymerization occurs after the first exposure via“print-through.” Kambly, for example, reports that print-through maypropagate up to 4 to 6 layers beneath the exposed surface.⁵ Whenconsidering the fabrication of GSS, techniques may be developed toreduce incremental curing from print-through in order to maintain thedegree of conversion at or below the gel point. ⁴K. C. Wu and J. W.Halloran, “Photopolymerization monitoring of ceramic stereolithographyresins by FTIR methods,” Journal of Materials Science, vol. 40, pp.71-76, 2005.⁵K. Kambly, “Characterization of Curing Kinetics andPhotopolymerization Shrinkage in Ceramic-Loaded Photocurable Resins forLarge Area Maskless Photopolymerization,” M.S. Thesis, MechanicalEngineering, Georgia Institute of Technology, Atlanta, 2009.

In addition to selecting the grayscale values appropriate for GSS, aproper screening resolution may also be chosen, i.e. to determine if theexposure technique should be a grayscale exposure or within thehomogenous transition. The rationale behind fabricating GSS is touniformly increase the viscosity of the region surrounding theunsupported feature. Therefore, it is appropriate to select a screeningresolution within the grayscale exposure region, as the homogenoustransition does not tend to produce uniform layers. Therefore, thescreening resolution used for all investigations of GSS was HDS superfine to guarantee grayscale exposure.

To evaluate the effectiveness of GSS in LAMP, a challenge component wasdesigned. The side and front views of the challenge component are shownin FIG. 119a , where the build direction is from the bottom up and thewhite regions correspond to areas to be solidified by UV exposure. Thetest component consists of a base, side wall, overhang and anunsupported square column. As the build progresses there will eventuallybe an unsupported feature for which the effectiveness of GSS may beassessed. The unsupported feature was a square column which has a squareside length of 1360 μm and column height of 3 mm. The column wasseparated from the base by a distance of 1 mm, the side wall by 3.06 mmand the unsupported structure connects to the part through an overhang.

Overhanging structures present a challenge for LAMP. However,embodiments of the present invention relate to systems suitable formanufacturing unsupported features. Therefore, when the build reachedthe overhanging structure, additional exposures were conducted to ensurethe overhang would not obstruct the assessment of GSS for unsupportedfeatures. FIG. 119b shows the first method employed for GSS. In thisGSS, one grayscale level is selected for each layer and grayscaleexposure surrounds the entire column. The grayscale exposure regionconnects to the base, side wall overhang, and unsupported feature.

Results from the first trial are shown in FIGS. 120a-120e . Based on theprediction from the cure depth equation and degree of conversionmeasurements, the grayscale values investigated were 50%, 54%, 56%, 58%and 62% at a screening resolution of HDS super fine. The buildparameters, such as material recoating speed and exposure time were setto 30 mm/s and 170 ms, respectively. From these results, an “all ornothing” behavior was observed. For this trial, grayscale values of 50%and 54% were unable to fabricate any component of the unsupportedcolumn. However, when the grayscale value was increased to 56%, nearlyall the grayscale region polymerized to a degree of conversion whichcould not be easily removed. This trend continued to the 58% whitegrayscale value, where it may be seen that an even larger amount of GSSremained well adhered to both the side wall and the unsupported feature.For the grayscale value of 62%, the GSS is nearly a solid block.

This result demonstrates good agreement with the predictions based onthe degree of conversion measurements. A grayscale value of 60% waspredicted to be the upper limit for GSS and it may be seen that agrayscale value of 62% may have mechanical properties too similar to thetest component. This “all or nothing” behavior may be related toprint-through and material recoating speed. A grayscale value of 54% forthese build parameters, however, was not viscous enough to adhere to theprevious layer and survive recoating.

As a result, the GSS became an unsupported feature in the followinglayer and was accordingly removed during recoating. This indicates thatthe GSS must be successful for each layer. When grayscale values of 56%and greater were used, the GSS was strong enough to survive the materialrecoating process. Each additional layer induced incrementalpolymerization in the previous layers due to print-through. Since, thedegree of conversion from a single layer is below the gel point, thePCMS is within the autoacceleration stage of polymerization. This causesthe degree of conversion to rapidly increase with minimal energy dose.As a result, the degree of conversion within the GSS approaches a valuesimilar to an all white exposure.

Reports by Xia and Fang demonstrate similar behavior in theirinvestigation of GSS for projection microstereolithography.⁶ In theirtest component, the GSS was bonded to the test component. However, theGSS was able to be removed through a piranha solution, whichpreferentially etched the partially polymerized support structure at afaster rate than the test component. In light of these findings,selective etching was investigated for the challenge component with aGSS of 56% to determine if this technique was suitable for LAMP. Twosolvents appropriate for LAMP were tested, which were acetone and 3D101.Etching was conducted through sonication at room temperature for onehour. ⁶C. G. Xia and N. Fang, “Fully three-dimensional microfabricationwith a grayscale polymeric self-sacrificial structure,” Journal ofMicromechanics and Microengineering, vol. 19, November 2009.

Results from the etching investigation are shown in FIGS. 121a-121c .The test component in FIG. 121a shows the condition and dimensions ofthe component prior to etching. Individual components were used for eachetching experiment. FIGS. 121b and 121c show the condition of thecomponent after etching with acetone and 3D 101, respectively. Fromthese results, it may be seen that neither of the two etching techniquescompletely removed the GSS. In each case, the GSS remained bonded to theside wall and a significant portion of GSS surrounded the unsupportedcolumn. However, while portions of the GSS were etched, so was aproportional amount of the test component. It was found that as much as1.25 mm of the test component was etched from ultrasonic cleaning witheither acetone or 3D101. This shows that print-through may increase thedegree of conversion in the GSS similar to that of the test component.As a result, the GSS could not be selectively etched. Rather, both theGSS and test component were etched at a similar rate.

Important observations may be made from these initial GSSinvestigations. First, it may be seen that the GSS formed at grayscalevalues of 56% possessed a degree of conversion too high to be easilyremoved and the GSS could not be differentiated from the test component.Consequently, a lower grayscale is needed to generate a GSS with a lowerdegree of conversion. Second, a GSS could not be formed for grayscalevalues lower than 56%. From this result, it may be interpreted that theideal grayscale for fabricating support structures is betweenapproximately 54% and 56%. Alternatively, it could be interpreted thatthe degree of conversion for easy removal after fabrication is below theminimum degree of conversion required to survive material recoating forthe given build parameters. Third, during etching much of the GSSremained bonded to the sidewall.

In consideration of these observations, three improvements to thefabrication of GSS may be made. First, the recoating speed may bereduced from 30 mm/s to 10 mm/s and the exposure time may be increasedfrom 170 ms to 218 ms. A lower recoating speed may act to lower theminimum degree of conversion required to survive material recoating.Increasing the exposure time, on the other hand, enables a largerdifference in the degree of conversion between grayscale exposure andall white exposure.

Second, embodiments of the present invention may also comprise a noveltechnique of alternating grayscale values between successive layers wasdeveloped to minimize print-through in the GSS. This technique isdepicted in FIG. 119c . The technique consists of alternating thegrayscale values between successive layers from a high grayscale valueto a low grayscale value. For instance, consider the GSS of 56%presented in FIGS. 120a-120e . The high degree of conversion generatedfrom print-through could be reduced by reducing the grayscale of everyother layer within the GSS.

When the degree of conversion is below the gel point, due toautoacceleration, for example, a lower degree of conversion has a lowercorresponding polymerization rate, which is demonstrated in FIGS. 117aand 117b . As a result, the lower degree of conversion may act as abarrier to mediate incremental polymerization throughout the fabricationof GSS. In addition to developing this system and method forprint-through reduction, the connection of the GSS to the side wall maybe removed to increase the surface area which may be developed aftercompletion of the build. The gap separation between the GSS and the sidewall may be set to approximately 1 mm, and 2 mm of GSS may be used tosurround the column in all directions.

Results from these modifications are shown in FIGS. 122a-122e . For thisexperiment in alternating grayscale, the low grayscale value was heldconstant at 50% and the high grayscale value was investigated at 52%(b), 53% (c), 54% (d), and 56% (e). In addition, to the alternating GSS,a constant GSS of 50% is also shown in (a). The first row shows the testcomponents before developing with 3D101. It may be seen that the GSSappears much less viscous than GSS formed in the first trial shown inFIGS. 119a-119e . The second row shows the test component after rinsingwith a water jet using 3D101, which is a typical technique used toremove residual monomer. It may be seen that removal of the GSS revealsthe successful fabrication of the grayscale supported test component.

The success may be largely attributed to reducing the recoating rate,which reduces the minimum degree of conversion required to survive therecoating process. FIG. 122a shows that a GSS of 50% may fabricate anunsupported column. This shows that alternating GSS are not necessary tofabricate unsupported features. Rather, the critical parameter was thematerial recoating speed. However, it is demonstrated that alternatinggrayscale exposure within the GSS is an effective method for fabricatingunsupported geometries as well. The advantage of alternating GSS is themitigation of “all or nothing” behavior.

FIGS. 122a-122e show that alternating grayscale GSS expands the range ofgrayscale that may be used to fabricate the unsupported column. This isevidenced by FIG. 122e , where an alternating GSS of 50% and 56% wasused. Previously, a GSS with the use of a single grayscale value at 56%was unable to be easily removed due to significant print-through.However, inserting a grayscale value of 50% every other layer within theGSS enabled the successful fabrication of the unsupported feature andeasy removal of the GSS with standard development techniques. This showsthe ability of alternating grayscale to mitigate residual curing fromprint-through. This aspect increases the reliability of fabricatingunsupported geometries and may allow for more variation in buildparameters.

One aspect of the test component which should be noted is that theheight of the column. The column height was designed to be 3 mm, yet foreach GSS, the height of the column was ˜3.5 mm. This may be related toprint-through causing curing up to 5 layers beneath the column. When anall white exposure is projected on the layer above a grayscale exposure,the susceptibility of print-through is increased due to a higher lightintensity. Grayscale exposure consumes many of the inhibitor speciestypically present in unexposed monomer. As a result, any additionalexposure dose goes directly to polymerization, which causes the columnto be longer than the design value.

In order to produce more accurate unsupported features, an additionaldesign revision to the GSS may be performed, which may be seen in FIG.119d . In this design, grayscale exposure is removed from directlyunderneath the unsupported feature. This design feature attempts tomitigate print-through, since the inhibitors in the PCMS must beconsumed before curing may occur. As a result, the probability ofdeveloping additional thickness beneath the exposed layer is reduced,which could result in a more accurately built test component.

Results from a print-through mediated alternating GSS are shown in FIGS.123a and 123b . The test component shown was fabricated with alternatinggrayscale values of 50% and 70%. FIGS. 123a and 123b depict the GSSbefore development and the unsupported column which appears afterdevelopment, respectively.

The difference between alternating grayscale values for theprint-through mediated GSS are more disparate than the typicalalternating GSS, which may be related to the volume reduction of thegrayscale support. From this result, a larger gap between the base andthe unsupported feature may be seen, which results in a higher accuracyin the build direction. The column height was measured to be 3.2 mm.This indicates that print-through develops additional thicknesscorresponding to two layers beneath the column in the absence ofgrayscale support directly beneath the column (i.e., as opposed to 5layers when grayscale is beneath the column).

It may also be noted that more shifting occurred during the fabricationof the column, which resulted in a variable cross-section through thelength of the grayscale supported column. In addition, it may be seenthat some roughness in the base layer developed due to print-throughfrom the higher alternating grayscale value. These effects may befurther reduced by increasing the dimensions of the surroundinggrayscale. This may enable a smaller difference in the alternatinggrayscales, for example, and the high grayscale used could be reduced,which would eliminate bonding to the base layer. A lager volume of GSSsurrounding the column may also prevent shifting during materialrecoating.

The results of grayscale exposure for the fabrication of unsupportedgeometries in LAMP are discussed above showing that grayscale supportstructures may be used to fabricate unsupported geometries and may beeasily removed after completion of part fabrication using standarddevelopment techniques. Techniques used in microstereolithography, suchas selective etching, however, are not particularly applicable for GSSin LAMP. However, with the incorporation of novel GSS designs, such asalternating grayscale and print-through mediation, reliable and accurateunsupported features may be obtained.

Additionally, the GSS may be easily removed after part completionwithout mechanical methods, which is important for applications to LAMP.Many of the unsupported geometries encountered in airfoil molds arewithin the internal features of the mold. This technique of grayscalesupport structures holds promise for successfully fabricatingunsupported features within airfoil molds and thus expanding theversatility of LAMP.

When an airfoil mold is successfully fabricated with LAMP, very fewcracks are observed in the green bodies. As a result, the majority ofdefects generated during LAMP occur during binder burnout and sintering.BBO is a sensitive process of removing the structural component to forma fragile ceramic powder component ready for sintering. Some defectswhich may be generated during BBO are spalling, cracking, blisters, andvoids. To reduce these defects, the material composition may becarefully considered and heating rates should be sufficiently low.Additionally, it is important to remove substantially all of the binderbefore sintering to higher temperatures. Mitigation of defects duringbinder burnout and sintering has been the focus of many studies and theresults indicate that polymerization shrinkage may be a primarycontributing factor.

Reports by Bae and Halloran investigated the formation of cracks duringBBO and sintering in ceramic stereolithography, where dependence onhatch spacing and retracted hatch were investigated.⁷ From theseresults, it was found that a larger retracted hatch produced morecracks. This was attributed to residual uncured monomer near the surfaceof the mold. The mechanism associated with this observation was thermalinitiation of radical species inducing polymerization of the uncuredmonomer, which caused shrinkage and sites for defect propagation.Interestingly, little dependence on hatch spacing could be associated tothe observed horizontal and vertical cracks. ⁷C.-J. Bae, “INTEGRALLYCORED CERAMIC INVESTMENT CASTING MOLD FABRICATED BY CERAMICSTEREOLITHOGRAPHY,” PhD, Materials Science and Engineering, Universityof Michigan, 2008.

In LAMP, a uniform light intensity exposure is applied to a large area,which causes anomalous defects to form during BBO. One of thesebehaviors is “fissures,” which is shown in FIGS. 124a-124d . Whilelarge-scale defects that prevent functionality of the mold for castingare not present in green bodies, fissure precursors may be seen, whichare shown in FIG. 124a . Fissures formed during BBO are straight andparallel with the LAMP layers. Additionally, a periodicity of every 4, 6and 8 layers is observed throughout the airfoil mold.

The origin of these fissures with temperature was reported and evidenceof these features may be seen at temperatures as low as 148° C. withcracks first appearing at 220° C. Interestingly, this corresponds to thetemperature range where the ketone initiator undergoes thermaldecomposition to form radicals, which may polymerize residual uncuredmonomer within the mold. It may also be noted that significant weightloss does not occur until 300° C. This indicates that the resultingfissures are not due to pyrolysis.

FIG. 124b shows the state of the mold after heating to 193° C. From thisimage it appears that the fissures are formed during BBO, yet beforesignificant weight loss has occurred, corresponding to the potentialfissure precursors observed in the green body, which is confirmed inFIG. 124c . For closer inspection, FIG. 124d shows an expanded view of atypical fissure with a 6 layer period.

These observations provide a strong indication that the observedfissures are a result of polymerization shrinkage and the stressresulting thereof. During exposure of a single layer, the degree ofconversion will vary with depth. Consequently, a large gradient indegree of conversion could exist at the interface of adjacent layers.When the green body mold reaches temperatures sufficient to decomposethe ketone initiators, regions of lower degree of conversion polymerizeand shrink away from the adjacent layers. This effect is observed inFIG. 124d by the lines between each layer.

In addition to polymerization shrinkage, it is also important toconsider polymerization shrinkage stress. From FIG. 124a it may be seenthat periodic fissure precursors exists in the green body mold and BBOpropagates the pre-existing defect. These fissures may be related toshrinkage stress. In LAMP, two main aspects contribute to stressdevelopment from shrinkage: (1) single layer shrinkage stress and (2)multiple layer shrinkage stress. Schematics of these two mechanisms areshown in FIGS. 125a and 125 b.

When UV light is exposed to the PCMS, an incremental depth ispolymerized and undergoes shrinkage. As the exposure progresses, anadditional incremental element is polymerized. If there are no boundaryconditions applied, the linear contraction from polymerization shrinkagein the second incremental element will induce a curvature away from thelight source. This effect is demonstrated in FIG. 125a and has beenobserved experimentally in FIG. 126. However, in LAMP, a boundarycondition is placed on the layer to remain flat. As a result stress isgenerated between adjacent layers.

The second mechanism of stress generation develops with the exposure ofmultiple layers, which is shown in FIG. 125b . When an additional layerof PCMS is exposed to UV light, the linear contraction interacts withthe preceding layer. If no boundary conditions are applied, curvaturedevelops towards the light source. Multiple layer shrinkage stress willcontinue to develop deeper into the build due to print-through. It isinteresting to note that print-through in LAMP may penetrateapproximately 6 layers, which is quite similar to the periodicityobserved in the fissures. It may be hypothesized, therefore, that thefissures are the result of a stress relaxation from the accumulation ofshrinkage stress across multiple layers due to print-through.

In order to test this hypothesis, methods to reduce polymerizationshrinkage and polymerization shrinkage stress through grayscale wereinvestigated. Polymerization shrinkage has been directly related to thedegree of conversion, where a high degree of conversion corresponds to alarge volumetric shrinkage.⁸ Therefore, it could be concluded that toreduce the negative effects of polymerization, the degree of conversionmust be kept low. However, during BBO uncured and partially curedmonomer may potentially polymerize due to thermal decomposition of thephotoinitiator generating free radicals for polymerization, and due tothe nature of BBO, volumetric changes should be minimized to reducedefects. In addition, a high degree of conversion is necessary to ensureaccuracy of the airfoil mold dimensions. Due to these considerations,reducing the degree of conversion may not be a viable method formitigating potential shrinkage related defects resulting from BBO andsintering. Consequently, mitigation of shrinkage defects is preferablyaddressed through a novel technique to obtain a high degree ofconversion, while mitigating volumetric shrinkage. As discussed blwo,this may be accomplished through exploitation of exposure patternswithin the homogenous transition. ⁸D. C. Watts, “Reaction kinetics andmechanics in photo-polymerised networks,” Dental Materials, vol. 21, pp.27-35, 2005.

When the exposure pattern projected onto the surface of the PCMS iswithin the homogenous transition, the average degree of conversion maydecrease by more than 50% when compared to an all white exposure, asshown in FIG. 118. This indicates that the net mitigation of volumetricshrinkage may also be greater than 50%. When exposure patterns arewithin the homogenous transition, uncured or partially cured monomer isretained within the layer, which has been shown to reduce volumetricshrinkage stress through monomer migration.⁹ With the prospect ofhomogenous transition exposure mitigating the net effect of volumetricshrinkage and reducing shrinkage stress, this shows promise for reducingdefects in the green body mold. Since the origin of fissures anddelamination generally depends on the state of the green body mold,reducing defects in the green body may reduce these types of defectsduring BBO and sintering. ⁹P. D. Ganahl, “Structured illumination as aprocessing method for controlling photopolymerized coatingcharacteristics,” Ph.D. Thesis, Chemical and Biochemical Engineering,University of Iowa, 2007.

To investigate the effectiveness of this technique for mitigating thesetypes of defects, a test component was designed. The test component wasa hollow cylinder, which is shown in FIGS. 127a and 127c . The outerdiameter of the cylinder was set to 22 mm with a thickness of 3 mm andheight of 24 mm to simulate nominal dimensions used in airfoil molds.The hollow cylinders were fabricated with all white exposure and withthree screening resolutions within the homogenous transition. Thescreening techniques utilized were checkerboard patterns with squarelengths of 170 μm, 255 μm and 425 μm, which correspond to screeningresolutions near grayscale exposure, in the middle of the homogenoustransition, and near all white exposure, respectively. For eachscreening resolution, the layers were exposed in a staggered pattern sothat the exposed region was unexposed in the following layer and viceversa, which is shown in FIGS. 127b and 127 d.

The exposure times selected to ensure proper bonding between layers were278 ms, 274 ms and 274 ms for square lengths of 170 μm, 255 μm, 425 μm,respectively. Four samples for each screening resolution were examinedto obtain a statistical information and four all white cylinders werefabricated with an exposure time of 170 ms to serve as a reference.After fabrication, each mold was developed with 3D101. Followingdevelopment, the test cylinders were subjected to BBO and sintering,where the heating schedule is shown in Table 6.1. After sintering wascomplete, the mold was cooled to room temperature in one hour.

TABLE 0.1 Heating schedule for binder burnout and sintering heating peakholding rate temperature time (° C./min) (° C.) (hours) 5 260 0 3 300 00.5 350 2 0.5 475 0 3 600 0 12.5 1350 2

FIGS. 128a and 128b shows the result from fabrication of a test cylinderwith all white exposure. The image in 128 a shows the green body moldilluminated to enhance the detection of defects. The mold contained asmooth surface, but distinct defects were present in the green body.FIG. 128b shows an expanded view of a section of the surface withenhanced contrast to demonstrate the fissure precursor. It may be seenthat a similar periodicity to the mold shown in FIG. 124a develops inthe all white test cylinder. This indicates a high probability thatfissures will develop during BBO. In addition to the fissure precursors,a defect related to “shuffle” may be seen, which is related to theserpentine path traversed in LAMP during large area exposure. From thesedefects in the green body, it may be expected that fissures will developin the regions shown in FIG. 128b and the shuffle defect will becomemore apparent during BBO and sintering due to thermally initiatedpolymerization and subsequent shrinkage.

This expectation is verified in FIGS. 129a and 129b , which showsnumerous horizontal defects resulting from BBO and sintering of the allwhite exposure test cylinder. The brightness from these fissures ishigher compared to those in the green body, which indicate a largerdefect. In this sample there were 4 horizontal defects which propagatedthroughout the circumference of the cylinder accompanied with manylocalized fissures. It may be seen that fissures occur throughout theheight of the test cylinder, where the severity of the defect varies,yet the spacing remains constant. FIG. 128b shows the regular spacing of4, 6, or 8 layers.

The results from FIGS. 129a and 129b show that fissures occur in thetest cylinder during BBO and sintering, which was predicted from theexistence of fissure precursors in the green body. Therefore,comparisons may be made regarding the effectiveness of homogenoustransition exposure for reducing or enhancing these defects. FIGS.130a-130c show the green body molds for cylinders fabricated withcheckerboard exposure at square lengths of 170 μm (a), 255 μm (b), and425 μm (c). In each screening resolution the surface roughness increasedcompared to the all white cylinder. In addition, spalling is observedand portions of the outer surface were removed during development. Theseeffects result due to the limited connectivity of the cured portionswithin the cylinder and the lack of a smooth outer surface. However, nofissure precursors could be discerned from the captured images. Thisindicates that fissures should not develop during BBO and sintering.

In addition to the absence of fissure precursors in the green bodies,the absence of a shuffle pattern defect may also be noted. By observingthe expanded views and enhancing the contrast, it may be seen thatvertical lines appear on the cylinder surfaces, which could lead to theformation of vertical defects during BBO and sintering. The verticalfeatures resulting from a square length of 170 μm appear less straight,when compared to cylinder with a square length of 255 μm and 425 μm, andare irregularly spaced. For the square lengths in FIGS. 130b and 130c ,the spacing is substantially constant and the lines are straight andparallel to the build direction. Also, it may be seen that the spacingbetween vertical lines is larger and with higher contrast for a squarelength of 425 μm compared to a square length of 255 μm. The length ofthe spacing was found to be equivalent to the square length utilized inthe exposure method, which indicates that the lines are a characteristicof the exposure technique.

These observations from the green body cylinders show promise formitigating fissures and shuffle defects since their precursors were notobserved. However, the exposure pattern introduced vertical lines and anuneven surface into the green bodies, which could cause the formation ofother defects apart from fissures and shuffle. FIGS. 131a-131c show theeffects of BBO and sintering on the test cylinders fabricated using astaggered checkerboard exposure with square length of 170 μm (a), 255 μm(b), and 425 μm (c).

Each screening resolution clearly has notably fewer long rangehorizontal fissures. FIG. 131a shows greatest number of long rangehorizontal fissures. However, these were the primary horizontal defectsobserved, in contrast to the all white exposure in which numeroushorizontal defects of smaller length were observed. When examining thescreening resolution with a square length of 255 μm and 425 μm, no longrange horizontal defects were observed.

Further inspection of the cylinder with a square length of 425 μm showsthat short range fissures may have developed. For both 170 μm and 425 μmsquare length screening resolution, the film is approaching homogeneity.In the case of 170 μm square length, the layer is near a homogenousgrayscale exposure and for a 425 μm square length, the layer is near ahomogenous all white exposure. From this consideration, a 455 μm mayhave mitigated features most efficiently due to its location in thecenter of the homogenous transition. These results indicate that aproper selection of homogenous transition exposure may be a viabletechnique for reducing fissures and delamination. For the examinedscreening resolution, a square length of 255 μm performed mostefficiently at reducing all types of defects including fissures.

When considering the other defects, it may be seen that while theshuffle defect was not observed in the green body cylinders, the defectdevelops in each investigated screening resolution. However, theintensity of the light projecting for the shuffle defect is less thanthe intensity seen in the all white cylinders and the feature is morepoorly defined. As a result, homogenous transition exposure did noteliminate the shuffle defect, but may have reduced it effects, whichcould be attributed to local shrinkage. Another effect which was notdetected in the green test cylinder is shown in the expanded views ofFIGS. 131a-131c . In the green cylinders with alternating checkerboardexposure, “continuous” vertical lines were observed. However, atransformation to “dotted” lines occurred as a result of BBO andsintering. This effect may be attributed to polymerization shrinkageresulting from thermal initiation of radicals and polymerization priorto pyrolysis. As a result, homogenous transition exposure may haveconverted the large scale fissures seen in all white exposure toisolated “micro-fissures,” which prevented the accumulation of shrinkageto produce larger defects.

Due to the vertical ordering of these micro-fissures, stress relaxationmay occur vertically. Investigations into vertical cracks are shown inFIGS. 132a-132d which show test cylinders where significant verticalcracks developed for each exposure technique. The largest verticalcracks occurred for screening resolutions with a square length of 455 μm(FIG. 132d ) where vertical cracks acted to split the test cylinder in 2of the 4 investigated samples at that screening resolution. Checkerboardpatterns with square lengths 170 μm (FIG. 132b ) also resulted in longrange cracks. For this sample it appears that a horizontal defectprevented further propagation of the vertical crack. For the all whiteexposure cylinder many horizontal fissures occupied the sample, which isshown in FIG. 132a . As a result, large scale vertical cracks werereduced and the sample contained many small vertical cracks. FIG. 132cshowed the least vertical cracks (both large and small scale), whichcorresponds to a checkerboard exposure with a square length of 255 μm.

1. A system for fabricating a three-dimensional object, the systemcomprising: a photosensitive medium adapted to change states uponexposure to a light source; an optical imaging system, configured tomove above the photosensitive medium, and having the light source and aspatial light modulator; a control system for controlling movement ofthe optical imaging system.
 2. (canceled)
 3. The system of claim 1, theoptical imaging system comprising a plurality of light sources andcomprising a plurality of spatial light.
 4. The system of claim 1, thephotosensitive medium selected from the group consisting of: aphotopolymer, a polymer-ceramic matrix, a polymer-ceramic precursormatrix, and mixtures thereof.
 5. (canceled)
 6. The system of claim 1,the spatial light modulator comprising a digital micromirror device. 7.The system of claim 1, the spatial light modulator selected from thegroup consisting of: a liquid crystal display, a grating light valve,and a digital mirror device.
 8. The system of claim 1, the spatial lightmodulator comprising a digital mirror device having a plurality ofpixels, each pixel configured to reflect light from the light source tothe projection lens in a first state and away from the projection lensin a second state.
 9. The system of claim 1, the light source comprisingan ultraviolet light source.
 10. The system of claim 9, the ultravioletlight source selected from the group consisting of: a mercury vaporlamp, xenon lamp, violet laser diode, diode pumped solid state laser,frequency-tripled Nd:YAG laser, and XeF excimer laser.
 11. The system ofclaim 1, wherein the optical imaging system further comprises aprojection lens having a reduction ratio between about 1 and about 50.12. The system of claim 1, further comprising a plurality of spatiallight modulators.
 13. The system of claim 1, further comprising an XYmotion stage with sub-micron position resolution, configured to move theoptical imaging system.
 14. A method, comprising: moving an opticalimaging system over a first surface of a photosensitive medium; andprojecting, with the optical imaging system, an image of a cross-sectionof a three-dimensional object onto a portion of the first surface of thephotosensitive medium while the optical imaging system is moving. 15.The method of claim 14, wherein the optical imaging system comprises apulsed light source, wherein the optical imaging system receives aplurality of images corresponding to portions of the cross section, andwherein the optical imaging system projects a single image from theplurality of images with each pulse of the pulsed light source on to thefirst surface of the photosensitive medium.
 16. The method of claim 14,further comprising the step of sweeping a layer of the photosensitivemedium across the first surface of the photosensitive medium to producea second surface of the photosensitive medium.
 17. The method of claim14, wherein the step of projecting an image of a cross section comprisesprojecting a screened grayscale image.
 18. The method of claim 0,wherein the screened grayscale image is produced using a halftoneprocess.
 19. The method of claim 0, wherein the screened grayscale imageis produced using a stochastic screening process.
 20. A method ofadditive manufacturing, comprising: slicing a digital model of athree-dimensional object into a plurality of slices, each slice having across-section; generating a build cross section by filling atwo-dimensional image having a predetermined size with a plurality ofcopies of a first cross-section selected from the group of crosssections. adding to the build cross section a conformal lattice to fillspace in the build cross section between the plurality of copies of thefirst cross-section. curing a portion of a photosensitive mediumcorresponding to the build cross-section to produce a layer of aplurality of three-dimensional objects.
 21. The method of claim 20,further comprising adding to the build cross-section a plurality ofbreak lines between the copies of the first cross-section.
 22. Themethod of claim 20, further comprising adding to the build cross-sectiona tank wall to the perimeter of the two-dimensional image.